Manager: Scot Symon
Home: Ibrox Stadium
Division One Winners: Hearts
Scottish Cup Winners: Clyde
League Cup Winners: Celtic
Match Results
| Round | Competition | Date | Venue | Outcome | Opponents | For | Agt | Crowd | ||
| Section 2 | League Cup | Aug | 10 | Sat | H | W | St Mirren | 6 | 0 | 55,000 |
| Section 2 | League Cup | 14 | Wed | a | W | Partick Thistle | 1 | 0 | 35,000 | |
| Section 2 | League Cup | 17 | Sat | H | W | Raith Rovers | 4 | 3 | 47,000 | |
| Section 2 | League Cup | 24 | Sat | a | W | St Mirren | 4 | 0 | 23,000 | |
| Section 2 | League Cup | 28 | Wed | H | L | Partick Thistle | 0 | 3 | 40,000 | |
| Section 2 | League Cup | 31 | Sat | a | L | Raith Rovers | 3 | 4 | 24,000 | |
| Qualifying | European Cup | Sep | 4 | Wed | H | W | St Etienne | 3 | 1 | 85,000 |
| Division 1 | 7 | Sat | H | W | Queen of the South | 4 | 2 | 25,000 | ||
| Quarter | League Cup | 11 | Wed | a | L | Kilmarnock | 1 | 2 | 26,803 | |
| Quarter | League Cup | 14 | Sat | H | W | Kilmarnock | 3 | 1 | 78,000 | |
| Division 1 | 21 | Sat | H | L | Celtic | 2 | 3 | 60,000 | ||
| Qualifying | European Cup | 25 | Wed | a | L | St Etienne | 1 | 2 | 35,000 | |
| Semi | League Cup | 28 | Sat | n | W | Brechin City | 4 | 0 | 28,453 | |
| Division 1 | Oct | 12 | Sat | a | W | St Mirren | 3 | 1 | 30,000 | |
| Final | League Cup | 19 | Sat | n | L | Celtic | 1 | 7 | 82,293 | |
| Division 1 | 26 | Sat | H | L | Hearts | 2 | 3 | 62,000 | ||
| Division 1 | Nov | 2 | Sat | a | W | Queen's Park | 4 | 2 | 30,824 | |
| Division 1 | 9 | Sat | H | L | Kilmarnock | 3 | 4 | 45,000 | ||
| Division 1 | 16 | Sat | H | W | Clyde | 2 | 0 | 65,000 | ||
| Division 1 | 23 | Sat | a | W | Falkirk | 4 | 0 | 22,000 | ||
| 1st | European Cup | 27 | Wed | H | L | AC Milan | 1 | 4 | 85,000 | |
| Division 1 | 30 | Sat | H | D | East Fife | 3 | 3 | 26,000 | ||
| Division 1 | Dec | 7 | Sat | a | D | Motherwell | 2 | 2 | 25,000 | |
| 1st | European Cup | 11 | Wed | a | L | AC Milan | 0 | 2 | 3,000 | |
| Division 1 | 14 | Sat | a | W | Dundee | 2 | 1 | 20,000 | ||
| Division 1 | 21 | Sat | H | W | Third Lanark | 5 | 1 | 22,000 | ||
| Division 1 | 28 | Sat | a | W | Aberdeen | 2 | 1 | 21,000 | ||
| Division 1 | Jan | 1 | Wed | a | W | Celtic | 1 | 0 | 50,000 | |
| Division 1 | 2 | Thu | H | W | Partick Thistle | 2 | 0 | 30,000 | ||
| Division 1 | 4 | Sat | a | D | Queen of the South | 1 | 1 | 13,000 | ||
| Division 1 | 11 | Sat | H | W | Hibs | 3 | 1 | 47,000 | ||
| Division 1 | 18 | Sat | a | W | Airdrie | 4 | 3 | 20,000 | ||
| 1st | Scottish Cup | Feb | 1 | Sat | a | W | Cowdenbeath | 3 | 1 | 16,866 |
| 2nd | Scottish Cup | 15 | Sat | a | W | Forfar Athletic | 9 | 1 | 8,066 | |
| Division 1 | 22 | Sat | H | W | Queen's Park | 5 | 1 | 30,000 | ||
| 3rd | Scottish Cup | Mar | 1 | Sat | a | W | Dunfermline | 2 | 1 | 24,377 |
| Division 1 | 8 | Sat | a | W | Clyde | 3 | 1 | 31,500 | ||
| Division 1 | 10 | Mon | a | D | Kilmarnock | 3 | 3 | 15,335 | ||
| Quarter | Scottish Cup | 15 | Sat | a | W | Queen of the South | 4 | 3 | 23,000 | |
| Division 1 | 19 | Wed | H | W | Falkirk | 3 | 2 | 25,000 | ||
| Division 1 | 22 | Sat | a | W | East Fife | 1 | 0 | 12,000 | ||
| Division 1 | 29 | Sat | H | D | Motherwell | 2 | 2 | 40,000 | ||
| Semi | Scottish Cup | Apr | 5 | Sat | n | D | Hibs | 2 | 2 | 76,727 |
| Replay | Scottish Cup | 9 | Wed | n | L | Hibs | 1 | 2 | 75,000 | |
| Division 1 | 12 | Sat | a | W | Third Lanark | 5 | 1 | 36,000 | ||
| Division 1 | 16 | Wed | H | W | Raith Rovers | 4 | 1 | 16,000 | ||
| Division 1 | 21 | Mon | a | L | Hibs | 1 | 3 | 25,000 | ||
| Division 1 | 23 | Wed | a | W | Raith Rovers | 3 | 1 | 10,000 | ||
| Division 1 | 26 | Sat | H | W | Aberdeen | 5 | 0 | 15,000 | ||
| Division 1 | 28 | Mon | H | W | St Mirren | 1 | 0 | |||
| Division 1 | 30 | Wed | a | L | Hearts | 1 | 2 | 30,000 | ||
| Division 1 | May | 3 | Sat | H | L | Airdrie | 1 | 2 | 25,000 | |
| Division 1 | 5 | Mon | a | W | Partick Thistle | 2 | 1 | 6,500 | ||
| Division 1 | 10 | Sat | H | L | Dundee | 0 | 1 | 11,000 |