| Manager | David Meiklejohn (Died 22nd August 1959) Willie Thornton (Appointed 24th September 1959) |
| Final League Position | 10th in the 1st Division ?th in Reserve League |
| Club Directory | |
| Squad List Team Group |
|
| Top Goalscorer |
| Date | Opposition | Competition | Result | Scorers | Attendance | |||
| Aug | 8 | AIRDRIEONIANS | League Cup Section 1 | 0-0 | – | 18,000 | ||
| Aug | 12 | Celtic | League Cup Section 1 | 2-1 | Wilson, Fleming | 25,000 | ||
| Aug | 15 | Raith Rovers | League Cup Section 1 | 0-2 | – | 12,000 | ||
| Aug | 19 | ARBROATH | 1st Division | 2-0 | Donlevy (Pen), Wilson | 8,000 | ||
| Aug | 22 | Airdrieonians | League Cup Section 1 | 0-4 | – | 6,000 | ||
| Aug | 26 | CELTIC | League Cup Section 1 | 0-2 | – | 20,000 | ||
| Aug | 29 | RAITH ROVERS | League Cup Section 1 | 1-3 | Keenan | 10,000 | ||
| Aug | 31 | CLYDE | Glasgow Cup 1st Round | 2-2 | Smith, McParland | ? | ||
| Sep | 5 | Clyde | 1st Division | 0-1 | – | 8,000 | ||
| Sep | 12 | THIRD LANARK | 1st Division | 2-0 | Donlevy (Pen), Smith | 18,000 | ||
| Sep | 15 | Clyde | Glasgow Cup 1st Round Replay | 4-3 | Harvey, Brown, Thomson, Fleming | 5,000 | ||
| Sep | 19 | Aberdeen | 1st Division | 2-5 | Smith, Fleming | 13,000 | ||
| Sep | 26 | RANGERS | 1st Division | 0-3 | – | 29,000 | ||
| Sep | 28 | Rangers | Glasgow Cup Final | 1-2 | Davidson | 38,807 | Played at Hampden | |
| Oct | 3 | Motherwell | 1st Division | 0-4 | – | 12,000 | ||
| Oct | 10 | KILMARNOCK | 1st Division | 3-2 | Fleming (2), Wright | 15,000 | ||
| Oct | 17 | Raith Rovers | 1st Division | 2-1 | McParland, Smith | 5,000 | ||
| Oct | 21 | Dumbarton | Friendly | 3-5 | Goldie, Donlevy, Wright | ? | ||
| Oct | 24 | STIRLING ALBION | 1st Division | 1-0 | Fleming | 10,000 | ||
| Oct | 31 | Dunfermline Athletic | 1st Division | 3-3 | Smith, McParland, Thomson | 7,000 | ||
| Nov | 7 | Heart of Midlothian | 1st Division | 3-5 | Smith (3) | 25,000 | ||
| Nov | 14 | DUNDEE | 1st Division | 0-5 | – | 8,000 | ||
| Nov | 21 | Airdrieonians | 1st Division | 0-3 | – | 5,000 | ||
| Nov | 28 | CELTIC | 1st Division | 3-1 | Smith (2),Fleming | 22,000 | ||
| Dec | 5 | Ayr United | 1st Division | 1-4 | Simpson | 7,500 | ||
| Dec | 12 | ST MIRREN | 1st Division | 4-2 | Simpson, McParland, Donlevy (Pen), Devine | 12,000 | ||
| Dec | 19 | HIBERNIAN | 1st Division | 2-10 | Smith (2) | 11,000 | ||
| Dec | 26 | Arbroath | 1st Division | 2-2 | McParland, OG (Young) | 4,228 | ||
| Jan | 1 | CLYDE | 1st Division | 0-1 | – | 11,000 | ||
| Jan | 2 | Third Lanark | 1st Division | 2-1 | Smith, Nimmo | 8,000 | ||
| Jan | 9 | ABERDEEN | 1st Division | 1-0 | Nimmo | 12,000 | ||
| Jan | 16 | Rangers | 1st Division | 1-1 | Fleming | 40,000 | ||
| Jan | 23 | MOTHERWELL | 1st Division | 1-2 | Fleming | 18,000 | ||
| Jan | 30 | East Fife | Scottish Cup 1st Round | 2-0 | McParland, OG (Stewart) | 3,475 | ||
| Feb | 6 | Kilmarnock | 1st Division | 1-5 | Nimmo | 16,000 | ||
| Feb | 13 | Dundee United | Scottish Cup 2nd Round | 2-2 | Devine, OG | 14,000 | ||
| Feb | 17 | DUNDEE UNITED | Scottish Cup 2nd Round Replay | 4-1 | Smith (3), Hogan | 9,500 | ||
| Feb | 20 | RAITH ROVERS | 1st Division | 1-0 | Devine | 7,000 | ||
| Feb | 27 | QUEEN OF THE SOUTH | Scottish Cup 3rd Round | 3-2 | Smith, McParland (2) | 12,000 | ||
| Mar | 2 | Stirling Albion | 1st Division | 1-2 | Fleming | 3,000 | ||
| Mar | 5 | DUNFERMLINE ATHLETIC | 1st Division | 2-0 | Smith (2) | 8,000 | ||
| Mar | 12 | Celtic | Scottish Cup 4th Round | 0-2 | – | 41,000 | ||
| Mar | 15 | HEART OF MIDLOTHIAN | 1st Division | 1-2 | Hastings | 7,000 | ||
| Mar | 19 | Dundee | 1st Division | 0-3 | – | 5,500 | ||
| Mar | 26 | AIRDRIEONIANS | 1st Division | 0-3 | – | 5,000 | ||
| Apr | 12 | Celtic | 1st Division | 4-2 | Smith (3), McParland | 22,000 | ||
| Apr | 16 | AYR UNITED | 1st Division | 3-1 | Donlevy (Pen), Hastings, Fleming | 7,500 | ||
| Apr | 23 | St Mirren | 1st Division | 4-2 | McParland (3), Fleming | 8,000 | ||
| Apr | 30 | Hibernian | 1st Division | 2-2 | Ewing,Fleming | 3,000 | ||
| May | 7 | Clachnauddin / Inverness Thistle XI | Friendly | 4-0 | Hastings, Hogan, Smith, Fleming | ? | ||
| May | 9 | THIRD LANARK | Glasgow Charity Cup 1st Round | 3-2 | McParland (2), Smith | 3,000 | ||
| May | 11 | Rangers | Glasgow Charity Cup Final | 0-2 | – | 8,296 | Played at Hampden | |
| Others: | ||||||||
| Aug | 8 | Airdrieonians | Reserve League Cup | 1-1 | ? | |||
| Aug | 12 | CELTIC | Reserve League Cup | 0-3 | – | |||
| Aug | 15 | RAITH ROVERS | Reserve League Cup | 2-2 | L Thomson, Unknown | |||
| Aug | 19 | ARBROATH | Reserve League | 0-5 | – | |||
| Aug | 21 | AIRDRIEONIANS | Reserve League Cup | |||||
| Aug | 25 | Celtic | Reserve League Cup | 0-6 | – | |||
| Sep | 4 | CLYDE | Reserve League | 2-2 | Ferns, Brown (Pen) | |||
| Sep | 19 | ABERDEEN | Reserve League | 2-1 | Keenan, Unknown | |||
| Sep | 26 | Rangers | Reserve League | 1-2 | ? | |||
| Oct | 3 | MOTHERWELL | Reserve League | 2-1 | ? | |||
| Oct | 9 | Kilmarnock | Reserve League | 4-2 | Goldie (3), Keenan | |||
| Oct | 14 | Hibernian | 2nd XI Cup 2nd Round | 1-2 | Goldie | |||
| Oct | 17 | RAITH ROVERS | Reserve League | 3-3 | Thomson, Brown, Unknown | |||
| Oct | 24 | Stirling Albion | Reserve League | 0-2 | – | |||
| Oct | 31 | DUNFERMLINE ATHLETIC | Reserve League | 0-1 | – | |||
| Nov | 7 | HEART OF MIDLOTHIAN | Reserve League | 2-4 | ? | |||
| Nov | 14 | Dundee | Reserve League | 0-3 | – | |||
| Nov | 21 | AIRDRIEONIANS | Reserve League | 5-1 | Nimmo (2), Devine, Unknown x 2 | |||
| Nov | 27 | Celtic | Reserve League | 0-1 | – | |||
| Dec | 12 | St Mirren | Reserve League | 2-2 | Nimmo, Unknown | |||
| Dec | 12 | Hamilton Academical | Friendly | ? | ? | |||
| Dec | 19 | Hibernian | Reserve League | 1-5 | W Thomson | |||
| Dec | 19 | East Stirlingshire | Friendly | 1-3 | ? | |||
| Jan | 2 | THIRD LANARK | Reserve League | 1-1 | Bain | |||
| Jan | 9 | Aberdeen | Reserve League | 2-0 | Simpson, Unknown | |||
| Jan | 13 | DUMBARTON | Friendly | ? | – | |||
| Jan | 15 | RANGERS | Reserve League | 1-3 | Wilson | |||
| Jan | 23 | Motherwell | Reserve League | 2-4 | Simpson (2) | |||
| Feb | 4 | KILMARNOCK | Reserve League | 1-0 | Trialist | |||
| Feb | 12 | AYR UNITED | Reserve League | 2-2 | Nimmo, Thomson | |||
| Mar | 1 | STIRLING ALBION | Reserve League | 1-2 | Simpson | |||
| Mar | 5 | Dunfermline Athletic | Reserve League | 2-2 | Unknown (2) | |||
| Mar | 12 | Heart of Midlothian | Reserve League | 1-2 | Unknown | |||
| Mar | 18 | DUNDEE | Reserve League | 0-3 | – | |||
| Mar | 26 | Airdrieonians | Reserve League | 1-2 | ? | |||
| Mar | 28 | SCOTLAND YOUTH SELECT | Friendly | ? | ? | |||
| Apr | 13 | Clyde | Reserve League | 3-1 | Unknown x 3 | |||
| Apr | 16 | Ayr United | Reserve League | 4-2 | Simpson, Ferns, Unknown x 2 | |||
| Apr | 23 | ST MIRREN | Reserve League | 2-2 | Ferns, Unknown | |||
| Apr | 29 | HIBERNIAN | Reserve League | 0-4 | – | |||