Manager: Bill Struth
Home: Ibrox Stadium
Division A Winners: Hibs
Scottish Cup Winners: Motherwell
League Cup Winners: Dundee
Match Results
| Round | Competition | Date | Venue | Outcome | Opponents | For | Agt | Crowd | ||
| Section D | League Cup | Aug | 11 | Sat | a | D | East Fife | 0 | 0 | 18,500 |
| Section D | League Cup | 15 | Wed | H | W | Aberdeen | 2 | 1 | 60,000 | |
| Section D | League Cup | 18 | Sat | a | W | Queen of the South | 3 | 0 | 19,000 | |
| Section D | League Cup | 25 | Sat | H | W | East Fife | 4 | 1 | 28,000 | |
| Section D | League Cup | 29 | Wed | a | L | Aberdeen | 1 | 2 | 28,000 | |
| Section D | League Cup | Sep | 1 | Sat | H | W | Queen of the South | 5 | 2 | 40,000 |
| Division A | 8 | Sat | H | W | Partick Thistle | 4 | 1 | 60,000 | ||
| Quarter | League Cup | 15 | Sat | a | L | Dunfermline | 0 | 1 | 20,000 | |
| Quarter | League Cup | 19 | Wed | H | W | Dunfermline | 3 | 1 | 45,000 | |
| Division A | 22 | Sat | H | D | Celtic | 1 | 1 | 86,000 | ||
| Division A | 29 | Sat | a | L | Dundee | 0 | 1 | 31,000 | ||
| Division A | Oct | 10 | Wed | H | D | East Fife | 1 | 1 | 20,000 | |
| Semi | League Cup | 13 | Sat | n | W | Celtic | 3 | 0 | 83,235 | |
| Division A | 20 | Sat | H | W | Hearts | 2 | 0 | 40,000 | ||
| Final | League Cup | 27 | Sat | n | L | Dundee | 2 | 3 | 95,325 | |
| Division A | Nov | 3 | Sat | a | D | Hibs | 1 | 1 | 55,000 | |
| Division A | 10 | Sat | H | W | St Mirren | 5 | 1 | 25,000 | ||
| Division A | 17 | Sat | a | L | Raith Rovers | 1 | 3 | 21,000 | ||
| Division A | 24 | Sat | H | W | Stirling Albion | 3 | 0 | 20,000 | ||
| Division A | Dec | 1 | Sat | H | D | Third Lanark | 1 | 1 | 20,000 | |
| Division A | 8 | Sat | a | W | Morton | 1 | 0 | 14,000 | ||
| Division A | 15 | Sat | H | W | Motherwell | 3 | 0 | 40,000 | ||
| Division A | 22 | Sat | a | W | Partick Thistle | 3 | 1 | 35,000 | ||
| Division A | 29 | Sat | H | W | Queen of the South | 3 | 2 | 30,000 | ||
| Division A | Jan | 1 | Tue | a | W | Celtic | 4 | 1 | 45,000 | |
| Division A | 2 | Wed | H | L | Dundee | 1 | 2 | 35,000 | ||
| Division A | 5 | Sat | a | L | East Fife | 1 | 2 | 18,000 | ||
| Division A | 12 | Sat | H | W | Airdrie | 1 | 0 | 45,000 | ||
| Division A | 19 | Sat | a | D | Hearts | 2 | 2 | 47,600 | ||
| Division A | 26 | Sat | a | W | St Mirren | 5 | 0 | 32,000 | ||
| Division A | Feb | 2 | Sat | H | W | Aberdeen | 3 | 2 | 40,000 | |
| 2nd | Scottish Cup | 9 | Sat | H | W | Elgin City | 6 | 1 | 36,324 | |
| Division A | 13 | Wed | H | D | Hibs | 2 | 2 | 45,000 | ||
| Division A | 16 | Sat | a | W | Airdrie | 1 | 0 | 24,000 | ||
| 3rd | Scottish Cup | 23 | Sat | a | W | Arbroath | 2 | 0 | 13,510 | |
| Division A | 27 | Wed | H | W | Raith Rovers | 1 | 0 | 20,000 | ||
| Division A | Mar | 1 | Sat | a | W | Stirling Albion | 5 | 1 | 14,000 | |
| Quarter | Scottish Cup | 8 | Sat | H | D | Motherwell | 1 | 1 | 82,000 | |
| Replay | Scottish Cup | 12 | Wed | a | L | Motherwell | 1 | 2 | 35,632 | |
| Division A | 15 | Sat | H | W | Morton | 1 | 0 | 35,000 | ||
| Division A | 22 | Sat | a | L | Motherwell | 1 | 2 | 22,200 | ||
| Division A | 29 | Sat | a | D | Queen of the South | 2 | 2 | 12,000 | ||
| Division A | Apr | 16 | Wed | a | D | Third Lanark | 1 | 1 | 15,000 | |
| Division A | 19 | Sat | a | D | Aberdeen | 1 | 1 | 20,000 |
