Manager: Bill Struth
Home: Ibrox Stadium
Division A Winners: Rangers
Scottish Cup Winners: Rangers
League Cup Winners: Dundee
Match Results
| Round | Competition | Date | Venue | Outcome | Opponents | For | Agt | Crowd | ||
| Section C | League Cup | Aug | 9 | Sat | a | L | Hearts | 0 | 5 | 41,000 |
| Section C | League Cup | 13 | Wed | H | W | Motherwell | 2 | 0 | 50,000 | |
| Section C | League Cup | 16 | Sat | H | W | Aberdeen | 3 | 1 | 40,000 | |
| Section C | League Cup | 23 | Sat | H | W | Hearts | 2 | 0 | 75,000 | |
| Section C | League Cup | 27 | Wed | a | D | Motherwell | 3 | 3 | 35,000 | |
| Section C | League Cup | 30 | Sat | a | W | Aberdeen | 2 | 1 | 35,000 | |
| Division A | Sep | 6 | Sat | a | W | St Mirren | 3 | 2 | 45,000 | |
| Quarter | League Cup | 13 | Sat | H | D | Third Lanark | 0 | 0 | 50,000 | |
| Quarter | League Cup | 17 | Wed | a | W | Third Lanark | 2 | 0 | 42,000 | |
| Division A | 20 | Sat | a | L | Celtic | 1 | 2 | 48,000 | ||
| Division A | 27 | Sat | H | W | Third Lanark | 4 | 1 | 25,000 | ||
| Semi | League Cup | Oct | 4 | Sat | n | L | Kilmarnock | 0 | 1 | 45,715 |
| Division A | 11 | Sat | H | L | Hibs | 1 | 2 | 65,000 | ||
| Division A | 18 | Sat | a | L | East Fife | 2 | 3 | 20,000 | ||
| Division A | Nov | 1 | Sat | H | W | Queen of the South | 3 | 1 | 20,000 | |
| Division A | 8 | Sat | a | W | Falkirk | 2 | 1 | 18,500 | ||
| Division A | 15 | Sat | a | W | Clyde | 6 | 4 | 28000 | ||
| Division A | 22 | Sat | H | W | Raith Rovers | 3 | 2 | 30,000 | ||
| Division A | Dec | 6 | Sat | H | W | Aberdeen | 4 | 0 | 35,000 | |
| Division A | 13 | Sat | a | D | Hearts | 2 | 2 | 27,000 | ||
| Division A | 20 | Sat | H | W | St Mirren | 4 | 0 | 35,000 | ||
| Division A | 27 | Sat | a | D | Airdrie | 2 | 2 | 20,000 | ||
| Division A | Jan | 1 | Thu | H | W | Celtic | 1 | 0 | 80,000 | |
| Division A | 3 | Sat | a | W | Third Lanark | 2 | 0 | 20,581 | ||
| Division A | 10 | Sat | H | D | Partick Thistle | 2 | 2 | 30,000 | ||
| Division A | 17 | Sat | a | D | Hibs | 1 | 1 | 60,500 | ||
| 1st | Scottish Cup | 24 | Sat | H | W | Arbroath | 4 | 0 | 44,000 | |
| Division A | 31 | Sat | H | W | East Fife | 4 | 0 | 52,000 | ||
| 2nd | Scottish Cup | Feb | 7 | Sat | a | W | Dundee | 2 | 0 | 43,024 |
| Division A | 14 | Sat | a | D | Dundee | 1 | 1 | 24,000 | ||
| 3rd | Scottish Cup | 21 | Sat | a | W | Morton | 4 | 1 | 23,000 | |
| Division A | 28 | Sat | H | W | Falkirk | 4 | 0 | 35,000 | ||
| Division A | Mar | 7 | Sat | H | L | Clyde | 1 | 2 | 55,000 | |
| Quarter | Scottish Cup | 14 | Sat | H | W | Celtic | 2 | 0 | 95,000 | |
| Division A | 18 | Wed | a | L | Raith Rovers | 1 | 3 | 18,000 | ||
| Division A | 21 | Sat | H | W | Motherwell | 4 | 1 | 35,000 | ||
| Division A | 28 | Sat | a | D | Aberdeen | 2 | 2 | 35,000 | ||
| Semi | Scottish Cup | Apr | 4 | Sat | n | W | Hearts | 2 | 1 | 116,262 |
| Division A | 6 | Mon | H | W | Hearts | 3 | 0 | 40,000 | ||
| Division A | 11 | Sat | a | W | Partick Thistle | 2 | 1 | 25,500 | ||
| Division A | 15 | Wed | H | W | Airdrie | 8 | 2 | 20,000 | ||
| Division A | 20 | Mon | a | W | Motherwell | 3 | 0 | 30,720 | ||
| Final | Scottish Cup | 25 | Sat | n | D | Aberdeen | 1 | 1 | 129,762 | |
| Replay | Scottish Cup | 29 | Wed | n | W | Aberdeen | 1 | 0 | 113,700 | |
| Division A | May | 2 | Sat | H | W | Dundee | 3 | 1 | 45,000 | |
| Division A | 7 | Thu | a | D | Queen of the South | 1 | 1 | 17,000 |
