Manager: Jock Wallace
Home: Ibrox Stadium
Premier Division Winners: Celtic
Scottish Cup Winners: Celtic
League Cup Winners: Aberdeen
Match Results
| Round | Competition | Date | Venue | Outcome | Opponents | For | Agt | Crowd | ||
| Section 4 | League Cup | Aug | 14 | Sat | H | W | St Johnstone | 5 | 0 | 31,000 |
| Section 4 | League Cup | 18 | Wed | a | D | Hibs | 1 | 1 | 26,000 | |
| Section 4 | League Cup | 21 | Sat | H | W | Montrose | 4 | 0 | 18,500 | |
| Section 4 | League Cup | 25 | Wed | H | W | Hibs | 3 | 0 | 45,000 | |
| Section 4 | League Cup | 28 | Sat | a | W | Montrose | 3 | 0 | 8,000 | |
| Section 4 | League Cup | Sep | 1 | Wed | a | W | St Johnstone | 1 | 0 | 4,070 |
| Premier Division | 4 | Sat | a | D | Celtic | 2 | 2 | 62,000 | ||
| Premier Division | 11 | Sat | H | D | Kilmarnock | 0 | 0 | 23,430 | ||
| 1st | European Cup | 15 | Wed | H | D | FC Zurich | 1 | 1 | 35,000 | |
| Premier Division | 18 | Sat | a | D | Hibs | 1 | 1 | 19,606 | ||
| Quarter | League Cup | 22 | Wed | H | D | Clydebank (New) | 3 | 3 | 15,000 | |
| Premier Division | 25 | Sat | H | W | Hearts | 4 | 2 | 25,000 | ||
| 1st | European Cup | 29 | Wed | a | L | FC Zurich | 0 | 1 | 28,500 | |
| Premier Division | Oct | 2 | Sat | a | D | Ayr Utd | 1 | 1 | 18,000 | |
| Replay | League Cup | 6 | Wed | a | D | Clydebank (New) | 1 | 1 | 10,000 | |
| Premier Division | 16 | Sat | H | W | Aberdeen | 1 | 0 | 21,800 | ||
| Replay | League Cup | 18 | Mon | H | D | Clydebank (New) | 0 | 0 | 15,000 | |
| Replay | League Cup | 19 | Tue | n | W | Clydebank (New) | 2 | 1 | 14,000 | |
| Premier Division | 23 | Sat | a | L | Motherwell | 1 | 3 | 15,857 | ||
| Semi | League Cup | 27 | Wed | n | L | Aberdeen | 1 | 5 | 20,990 | |
| Premier Division | 30 | Sat | a | L | Partick Thistle | 1 | 2 | 16,900 | ||
| Premier Division | Nov | 9 | Tue | H | W | Dundee Utd | 3 | 0 | 16,000 | |
| Premier Division | 13 | Sat | a | W | Kilmarnock | 4 | 0 | 14,717 | ||
| Premier Division | 20 | Sat | H | D | Hibs | 1 | 1 | 24,621 | ||
| Premier Division | 24 | Wed | H | L | Celtic | 0 | 1 | 43,500 | ||
| Premier Division | 27 | Sat | a | W | Hearts | 1 | 0 | 19,000 | ||
| Premier Division | Dec | 26 | Sun | H | W | Motherwell | 1 | 0 | 28,000 | |
| Premier Division | Jan | 1 | Sat | H | W | Partick Thistle | 1 | 0 | 20,000 | |
| Premier Division | 8 | Sat | H | W | Kilmarnock | 3 | 0 | 18,189 | ||
| Premier Division | 11 | Tue | a | L | Celtic | 0 | 1 | 60,000 | ||
| Premier Division | 19 | Wed | a | D | Aberdeen | 3 | 3 | 21,591 | ||
| Premier Division | 22 | Sat | H | W | Hearts | 3 | 2 | 19,700 | ||
| 3rd | Scottish Cup | 29 | Sat | H | W | Falkirk | 3 | 1 | 17,500 | |
| Premier Division | Feb | 5 | Sat | a | W | Ayr Utd | 2 | 0 | 12,800 | |
| Premier Division | 12 | Sat | H | L | Dundee Utd | 2 | 3 | 16,000 | ||
| Premier Division | 16 | Wed | a | D | Hibs | 0 | 0 | 12,452 | ||
| Premier Division | 19 | Sat | H | W | Aberdeen | 1 | 0 | 17,000 | ||
| 4th | Scottish Cup | 26 | Sat | H | W | Elgin City | 3 | 0 | 18,000 | |
| Premier Division | Mar | 5 | Sat | a | W | Motherwell | 2 | 0 | 15,468 | |
| Premier Division | 8 | Tue | a | D | Dundee Utd | 0 | 0 | 10,250 | ||
| Quarter | Scottish Cup | 12 | Sat | H | W | Motherwell | 2 | 0 | 35,572 | |
| Premier Division | 15 | Tue | a | L | Partick Thistle | 3 | 4 | 17,000 | ||
| Premier Division | 19 | Sat | H | D | Celtic | 2 | 2 | 55,500 | ||
| Premier Division | 23 | Wed | H | D | Ayr Utd | 1 | 1 | 10,000 | ||
| Premier Division | 26 | Sat | a | L | Kilmarnock | 0 | 1 | 8,037 | ||
| Semi | Scottish Cup | 30 | Wed | n | W | Hearts | 2 | 0 | 23,222 | |
| Premier Division | Apr | 2 | Sat | H | W | Hibs | 2 | 1 | 11,500 | |
| Premier Division | 9 | Sat | a | W | Hearts | 3 | 1 | 12,500 | ||
| Premier Division | 13 | Wed | H | W | Partick Thistle | 2 | 1 | 8,000 | ||
| Premier Division | 16 | Sat | H | W | Ayr Utd | 5 | 1 | 10,000 | ||
| Premier Division | 20 | Wed | H | W | Motherwell | 4 | 1 | 8,000 | ||
| Premier Division | 23 | Sat | a | W | Dundee Utd | 1 | 0 | 8,000 | ||
| Premier Division | 30 | Sat | a | L | Aberdeen | 1 | 2 | 13,484 | ||
| Final | Scottish Cup | May | 7 | Sat | n | L | Celtic | 0 | 1 | 54,252 |
