Manager: Bill Struth
Home: Ibrox Stadium
Division One Winners: Celtic
Scottish Cup Winners: Morton
Match Results
| Round | Competition | Date | Venue | Outcome | Opponents | For | Agt | Crowd | ||
| Division 1 | Aug | 16 | Tue | a | W | Third Lanark | 3 | 1 | 29,000 | |
| Division 1 | 20 | Sat | a | W | Clydebank (old) | 7 | 1 | 22,000 | ||
| Division 1 | 23 | Tue | H | W | Albion Rovers | 3 | 1 | 31,000 | ||
| Division 1 | 27 | Sat | H | W | Motherwell | 2 | 1 | 40,000 | ||
| Division 1 | Sep | 3 | Sat | a | W | St Mirren | 2 | 1 | 35,290 | |
| Division 1 | 10 | Sat | H | W | Kilmarnock | 1 | 0 | 20,000 | ||
| Division 1 | 19 | Mon | a | W | Hearts | 2 | 1 | 22,000 | ||
| Division 1 | 24 | Sat | H | W | Aberdeen | 1 | 0 | 26,000 | ||
| Division 1 | 26 | Mon | H | W | Clyde | 3 | 0 | 38,000 | ||
| Division 1 | Oct | 8 | Sat | H | L | Hearts | 0 | 2 | 40,000 | |
| Division 1 | 15 | Sat | a | W | Airdrie | 2 | 1 | 15,000 | ||
| Division 1 | 22 | Sat | H | D | Celtic | 1 | 1 | 50,000 | ||
| Division 1 | 29 | Sat | a | W | Queen's Park | 4 | 2 | 32,000 | ||
| Division 1 | Nov | 5 | Sat | a | D | Dundee | 0 | 0 | 39,000 | |
| Division 1 | 12 | Sat | H | D | Dumbarton | 1 | 1 | 16,000 | ||
| Division 1 | 19 | Sat | a | W | Morton | 2 | 1 | 20,000 | ||
| Division 1 | 26 | Sat | H | W | Hamilton Acas | 5 | 0 | 20,000 | ||
| Division 1 | Dec | 3 | Sat | a | L | Falkirk | 0 | 1 | 18,000 | |
| Division 1 | 10 | Sat | H | W | Third Lanark | 2 | 1 | 20,000 | ||
| Division 1 | 17 | Sat | a | W | Albion Rovers | 5 | 0 | 10,000 | ||
| Division 1 | 24 | Sat | a | D | Hibs | 0 | 0 | 25,000 | ||
| Division 1 | 26 | Mon | H | W | Dundee | 2 | 1 | 10,000 | ||
| Division 1 | 31 | Sat | H | W | St Mirren | 4 | 1 | 30,000 | ||
| Division 1 | Jan | 2 | Mon | a | D | Celtic | 0 | 0 | 60,000 | |
| Division 1 | 3 | Tue | H | D | Partick Thistle | 2 | 2 | 35,000 | ||
| Division 1 | 7 | Sat | a | W | Ayr Utd | 1 | 0 | 12,000 | ||
| Division 1 | 14 | Sat | H | L | Raith Rovers | 0 | 1 | 20,000 | ||
| Division 1 | 21 | Sat | a | D | Hamilton Acas | 0 | 0 | 20,000 | ||
| 1st | Scottish Cup | 28 | Sat | a | W | Inverness Clachnacuddin | 5 | 0 | 4,000 | |
| Division 1 | Feb | 4 | Sat | a | L | Motherwell | 0 | 2 | 10,000 | |
| 2nd | Scottish Cup | 11 | Sat | a | D | Albion Rovers | 1 | 1 | 20,000 | |
| Replay | Scottish Cup | 15 | Wed | H | W | Albion Rovers | 4 | 0 | 35,000 | |
| Division 1 | 18 | Sat | a | W | Partick Thistle | 1 | 0 | 53,000 | ||
| Division 1 | 21 | Tue | H | W | Clydebank (old) | 6 | 1 | 5,000 | ||
| 3rd | Scottish Cup | 25 | Sat | a | W | Hearts | 4 | 0 | 40,000 | |
| Division 1 | 28 | Tue | H | D | Falkirk | 0 | 0 | 18,000 | ||
| Division 1 | Mar | 4 | Sat | H | W | Morton | 3 | 0 | 18,000 | |
| Quarter | Scottish Cup | 11 | Sat | H | D | St Mirren | 1 | 1 | 67,700 | |
| Replay | Scottish Cup | 14 | Tue | a | W | St Mirren | 2 | 0 | 38,027 | |
| Semi | Scottish Cup | 25 | Sat | H | W | Partick Thistle | 2 | 0 | 60,000 | |
| Division 1 | 28 | Tue | H | W | Hibs | 2 | 0 | 13,000 | ||
| Division 1 | Apr | 1 | Sat | H | W | Ayr Utd | 2 | 0 | 20,000 | |
| Division 1 | 3 | Mon | a | W | Raith Rovers | 3 | 0 | 20,000 | ||
| Division 1 | 5 | Wed | a | D | Aberdeen | 0 | 0 | 20,000 | ||
| Division 1 | 8 | Sat | a | W | Dumbarton | 4 | 0 | 7,000 | ||
| Final | Scottish Cup | 15 | Sat | n | L | Morton | 0 | 1 | 70,000 | |
| Division 1 | 17 | Mon | H | W | Queen's Park | 2 | 1 | 15,000 | ||
| Division 1 | 22 | Sat | H | W | Airdrie | 3 | 0 | 18,000 | ||
| Division 1 | 24 | Mon | a | W | Kilmarnock | 2 | 1 | 12,000 | ||
| Division 1 | 29 | Sat | a | D | Clyde | 0 | 0 | 30,000 |
