Manager: Bill Struth
Home: Ibrox Stadium
Division A Winners: Hibs
Scottish Cup: Rangers
League Cup Winners: East Fife
Match Results
| Round | Competition | Date | Venue | Outcome | Opponents | For | Agt | Crowd | ||
| Section C | League Cup | Aug | 9 | Sat | H | W | Celtic | 2 | 0 | 80,000 |
| Division A | 13 | Wed | H | W | Third Lanark | 5 | 2 | |||
| Section C | League Cup | 16 | Sat | a | W | Third Lanark | 3 | 1 | 25,000 | |
| Section C | League Cup | 23 | Sat | H | W | Dundee | 3 | 0 | 25,000 | |
| Division A | 27 | Wed | a | W | Partick Thistle | 1 | 0 | 35,000 | ||
| Section C | League Cup | 30 | Sat | a | L | Celtic | 0 | 2 | 60,000 | |
| Section C | League Cup | Sep | 6 | Sat | H | W | Third Lanark | 3 | 0 | 20,000 |
| Section C | League Cup | 13 | Sat | a | D | Dundee | 1 | 1 | 39,000 | |
| Division A | 20 | Sat | H | W | Celtic | 2 | 0 | 50,000 | ||
| Quarter | League Cup | 27 | Sat | H | W | Stenhousemuir | 2 | 0 | 25,000 | |
| Semi | League Cup | Oct | 11 | Sat | n | L | Falkirk | 0 | 1 | 44,432 |
| Division A | 18 | Sat | H | W | Hibs | 2 | 1 | 55,000 | ||
| Division A | 25 | Sat | a | L | St Mirren | 1 | 2 | 24,000 | ||
| Division A | Nov | 1 | Sat | H | W | Airdrie | 3 | 0 | 15,000 | |
| Division A | 8 | Sat | a | W | Queen of the South | 3 | 0 | 21,000 | ||
| Division A | 15 | Sat | a | W | Clyde | 2 | 1 | 30,000 | ||
| Division A | 22 | Sat | H | D | Morton | 1 | 1 | 25,000 | ||
| Division A | 29 | Sat | a | W | Queen's Park | 4 | 1 | 28,000 | ||
| Division A | Dec | 6 | Sat | a | W | Hearts | 2 | 1 | 40,000 | |
| Division A | 13 | Sat | H | W | Aberdeen | 4 | 0 | 30,000 | ||
| Division A | 20 | Sat | a | W | Third Lanark | 1 | 0 | 20,000 | ||
| Division A | 25 | Thu | a | W | Dundee | 3 | 1 | 25,000 | ||
| Division A | 27 | Sat | H | W | Partick Thistle | 2 | 1 | 20,000 | ||
| Division A | Jan | 2 | Fri | a | W | Celtic | 4 | 0 | 60,000 | |
| Division A | 3 | Sat | H | W | Dundee | 2 | 1 | 35,000 | ||
| Division A | 10 | Sat | a | W | Falkirk | 5 | 1 | 22,000 | ||
| Division A | 17 | Sat | H | W | Motherwell | 2 | 0 | 35,000 | ||
| 1st | Scottish Cup | 24 | Sat | a | W | Stranraer | 1 | 0 | 6,000 | |
| Division A | 31 | Sat | a | L | Hibs | 0 | 1 | 52,750 | ||
| 2nd | Scottish Cup | Feb | 7 | Sat | H | W | Leith Athletic | 4 | 0 | 17,000 |
| Division A | 14 | Sat | H | W | St Mirren | 3 | 2 | 20,000 | ||
| 3rd | Scottish Cup | 21 | Sat | H | W | Partick Thistle | 3 | 0 | 68,000 | |
| Division A | 28 | Sat | H | L | Queen of the South | 2 | 3 | 34,000 | ||
| Quarter | Scottish Cup | Mar | 6 | Sat | H | W | East Fife | 1 | 0 | 90,000 |
| Division A | 13 | Sat | a | W | Morton | 1 | 0 | 18,000 | ||
| Division A | 20 | Sat | H | L | Queen's Park | 1 | 2 | 37,000 | ||
| Semi | Scottish Cup | 27 | Sat | n | W | Hibs | 1 | 0 | 143,570 | |
| Division A | 29 | Mon | H | D | Falkirk | 1 | 1 | |||
| Division A | Apr | 3 | Sat | a | D | Aberdeen | 1 | 1 | 43,800 | |
| Final | Scottish Cup | 17 | Sat | n | D | Morton | 1 | 1 | 131,975 | |
| Replay | Scottish Cup | 21 | Wed | n | W | Morton | 1 | 0 | 133,750 | |
| Division A | 24 | Sat | a | D | Motherwell | 1 | 1 | 25,000 | ||
| Division A | 26 | Mon | H | W | Clyde | 2 | 1 | |||
| Division A | May | 1 | Sat | a | W | Airdrie | 2 | 1 | 18,000 | |
| Division A | 3 | Thu | H | L | Hearts | 1 | 2 | 10,000 |
