| Manager | George Easton |
| Final League Position | 6th in 1st Division ?th in Scottish Alliance |
| Club Directory | |
| Team Group | |
| Squad List |
| Date | Opposition | Competition | Result | Scorers | Attendance | |||
| Aug | 19 | DUMBARTON | 1st Division | 1-0 | Kinloch | 15,000 | Postponed 17/08/20 due to waterlogged pitch | |
| Aug | 21 | Ayr United | 1st Division | 1-2 | McFarlane | 6,000 | ||
| Aug | 24 | Clydebank | 1st Division | 1-1 | Kinloch | 8,000 | ||
| Aug | 28 | RAITH ROVERS | 1st Division | 3-1 | Blair, Kerr (2) | 18,000 | ||
| Aug | 30 | Albion Rovers | 1st Division | 0-0 | – | 7,000 | ||
| Sep | 4 | ST MIRREN | 1st Division | 5-1 | Hamilton, Kinloch, Kerr, McMenemy, Salisbury | 15,000 | ||
| Sep | 8 | Raith Rovers | 1st Division | 0-1 | – | 8,060 | ||
| Sep | 11 | Motherwell | 1st Division | 4-0 | Hamilton, McMullian, Kerr, Blair | 8,000 | ||
| Sep | 18 | Clyde | Glasgow Cup Semi-Final | 0-1 | – | 20,000 | ||
| Sep | 25 | HAMILTON ACADEMICAL | 1st Division | 1-1 | Kerr | 18,000 | ||
| Sep | 27 | CLYDE | 1st Division | 2-1 | Kerr, Salisbury | 21,000 | ||
| Oct | 2 | Queen's Park | 1st Division | 1-1 | Kinloch | 10,000 | ||
| Oct | 9 | CLYDEBANK | 1st Division | 2-2 | Blair, Kerr | 25,000 | ||
| Oct | 16 | Rangers | 1st Division | 0-3 | – | 30,000 | ||
| Oct | 23 | HIBERNIAN | 1st Division | 3-2 | Blair, Kinloch, Kerr | 12,000 | ||
| Oct | 30 | Morton | 1st Division | 0-4 | – | 10,000 | ||
| Nov | 6 | Kilmarnock | 1st Division | 1-0 | Niven | 6,000 | ||
| Nov | 13 | FALKIRK | 1st Division | 2-1 | Salisbury, Lauder | 10,000 | ||
| Nov | 20 | Airdrieonians | 1st Division | 2-1 | Blair, Niven | 8,000 | ||
| Nov | 27 | QUEEN'S PARK | 1st Division | 5-0 | Blair, Kinloch (3), Niven | 15,000 | ||
| Dec | 4 | Dumbarton | 1st Division | 1-0 | McMullian | 4,000 | ||
| Dec | 11 | Celtic | 1st Division | 0-1 | – | 30,000 | ||
| Dec | 18 | DUNDEE | 1st Division | 2-1 | Blair (2) | 10,000 | ||
| Dec | 25 | Aberdeen | 1st Division | 3-0 | Blair (2), Salisbury | 13,000 | ||
| Jan | 1 | THIRD LANARK | 1st Division | 1-0 | Johnstone | 20,000 | ||
| Jan | 3 | RANGERS | 1st Division | 0-2 | – | 42,000 | ||
| Jan | 4 | St Mirren | 1st Division | 2-0 | Comrie, Johnstone | 9,000 | ||
| Jan | 8 | Heart of Midlothian | 1st Division | 0-1 | – | 12,000 | ||
| Jan | 15 | AIRDRIEONIANS | 1st Division | 0-0 | – | 15,000 | ||
| Jan | 22 | HEART OF MIDLOTHIAN | 1st Division | 0-0 | – | 10,000 | ||
| Jan | 29 | ALBION ROVERS | 1st Division | 0-0 | – | 20,000 | ||
| Feb | 5 | Hibernian | Scottish Cup 2nd Round | 0-0 | – | 32,000 | ||
| Feb | 8 | HIBERNIAN | Scottish Cup 2nd Round Replay | 0-0 | – | 25,000 | ||
| Feb | 12 | MORTON | 1st Division | 4-0 | Kinloch, McFarlane, Wilson, Bernard (Pen) | 15,000 | ||
| Feb | 15 | Hibernian | Scottish Cup 2nd Round 2nd Replay | 1-0 | McFarlane | 22,000 | Played at Celtic Park | |
| Feb | 19 | East Stirlingshire | Scottish Cup 3rd Round | 2-1 | Kinloch (2) | 8,000 | ||
| Feb | 22 | Clyde | 1st Division | 1-2 | Kinloch | 5,000 | ||
| Feb | 26 | KILMARNOCK | 1st Division | 1-1 | Salisbury | 12,000 | ||
| Mar | 5 | Motherwell | Scottish Cup 4th Round | 2-2 | McFarlane, Salisbury | 14,000 | ||
| Mar | 8 | MOTHERWELL | Scottish Cup 4th Round Replay | 0-0 | – | 25,000 | ||
| Mar | 12 | Dundee | 1st Division | 0-1 | – | 4,000 | ||
| Mar | 15 | Motherwell | Scottish Cup 4th Round 2nd Replay | 2-1 | McFarlane, Lauder | 10,000 | Played at Ibrox | |
| Mar | 19 | MOTHERWELL | 1st Division | 0-0 | – | 10,000 | ||
| Mar | 26 | Heart of Midlothian | Scottish Cup Semi-Final | 0-0 | – | 40,000 | Played at Ibrox | |
| Mar | 28 | CELTIC | 1st Division | 0-1 | – | 9,000 | Played at Ibrox | |
| Mar | 30 | HEART OF MIDLOTHIAN | Scottish Cup Semi-Final Replay | 0-0 | – | 27,000 | Played at Ibrox | |
| Apr | 2 | ABERDEEN | 1st Division | 2-2 | Harris, Salisbury | 12,000 | ||
| Apr | 5 | Heart of Midlothian | Scottish Cup Semi-Final 2nd Replay | 2-0 | Kinloch (2) | 27,000 | Played at Ibrox | |
| Apr | 8 | Hamilton Academical | 1st Division | 0-1 | – | 6,000 | ||
| Apr | 16 | Rangers | Scottish Cup Final | 1-0 | Blair | 28,294 | Played at Celtic Park | |
| Apr | 19 | Third Lanark | 1st Division | 0-1 | – | 8,000 | ||
| Apr | 23 | AYR UNITED | 1st Division | 0-0 | – | 15,000 | Joe Harris Benefit | |
| Apr | 26 | Falkirk | 1st Division | 2-1 | Kinloch, Blair | 4,500 | ||
| Apr | 27 | Hibernian | 1st Division | 0-2 | – | 6,000 | ||
| May | 7 | Celtic | Glasgow Charity Cup Semi-Final | 0-2 | – | 20,000 | ||
| Others: | ||||||||
| Sep | 4 | Rangers | Scottish Alliance | 2-1 | Unknown x 2 | |||
| Sep | 11 | THIRD LANARK | Scottish 2nd XI Cup 1st Round | 4-1 | R McFarlane, Comrie, Lauder (2) | |||
| Sep | 18 | MORTON | Scottish Alliance | 4-1 | Niven, Salisbury, Comrie, Robertson | |||
| Sep | 25 | Ayr United | Scottish Alliance | 2-2 | Unknown x 2 | |||
| Oct | 2 | ALBION ROVERS | Scottish Alliance | 1-2 | Bernard | |||
| Oct | 9 | Arbroath | Scottish Alliance | 2-3 | Salisbury, Unknown | |||
| Oct | 16 | Queen's Park Strollers | Scottish Alliance | 1-0 | Mackie | |||
| Oct | 23 | Hibernian | Scottish Alliance | 2-1 | Unknown x 2 | |||
| Oct | 30 | DUNDEE | Scottish Alliance | 4-1 | Niven, R McFarlane (2), Bernard | |||
| Nov | 6 | HIBERNIAN | Scottish Alliance | 1-1 | Comrie | |||
| Nov | 13 | QUEEN'S PARK STROLLERS | Scottish Alliance | 2-1 | McLaughlin, Niven | |||
| Nov | 20 | MOTHERWELL | Scottish Alliance | 1-2 | McIntosh | |||
| Dec | 4 | RANGERS | Scottish Alliance | 1-0 | Lauder | |||
| Dec | 11 | CELTIC | Scottish Alliance | 0-0 | – | |||
| Dec | 18 | Dundee | Scottish Alliance | 1-0 | McCourt | |||
| Dec | ? | ? | Scottish Alliance | ? | ? | |||
| Dec | ? | ? | Scottish Alliance | ? | ? | |||
| Jan | ? | ? | Scottish Alliance | ? | ? | |||
| Jan | 8 | AYR UNITED | Scottish Alliance | 3-1 | Unknown x 3 | |||
| Jan | 22 | Albion Rovers | Scottish Alliance | 0-2 | – | |||
| Jan | 29 | Aberdeen | Scottish Alliance | 2-3 | Unknown x 2 | |||
| Feb | 5 | THIRD LANARK | Scottish Alliance | 0-0 | – | |||
| Feb | ? | ? | Scottish Alliance | ? | ? | |||
| Feb | 19 | KILMARNOCK | Scottish Alliance | 2-0 | Unknown x 2 | |||
| Feb | ? | ? | Scottish 2nd XI Cup 2nd Round | ? | ? | |||
| Mar | 5 | FORFAR ATHLETIC | Scottish Alliance | 2-4 | McGraw, Anderson | |||
| Mar | 12 | Rangers | Scottish 2nd XI Cup 3rd Round | 0-2 | – | |||
| Mar | 19 | Motherwell | Scottish Alliance | 1-2 | Unknown | |||
| Apr | 9 | CLYDE | Scottish Alliance | 0-2 | – | |||
| Apr | 16 | Clyde | Scottish Alliance | 0-0 | – | |||
| Apr | 23 | Morton | Scottish Alliance | 0-4 | – | |||
| Apr | 30 | Forfar Athletic | Scottish Alliance | 4-2 | McLean, Salisbury (3) | |||
| ? | ? | ? | Scottish Alliance | ? | ? | |||
| ? | ? | ? | Scottish Alliance | ? | ? | |||
| ? | ? | ? | Scottish Alliance | ? | ? | |||
| ? | ? | ? | Scottish Alliance | ? | ? | |||
| Fives: | ||||||||
| 3rd July 1920 | Kilmarnock FC Sports Day | Unknown | ||||||
| 10th July 1920 | Partick Thistle Sports Day | Unknown | ||||||
| 31st July 1920 | Clydebank Sports Day | Unknown | ||||||
| 14th August 1920 | Celtic Sports Day | 1st Round | ||||||
Representative Honors for 1920-21
Kenny Campbell (Scotland) v Wales, Ireland
Joe Harris (Scottish League) v English League / (Scotland) v Wales, Ireland
Jimmy McMememy (Scottish League) v Celtic & Rangers XI
Jimmy McMullan (Glasgow) v Sheffield / (Scotland) v Wales, Ireland, England / (Scottish League) v Irish League, English League
Robert Millar (Alliance West) v Alliance East
William Robertson (Alliance West) v Alliance East