Manager: Bill Struth
Home: Ibrox Stadium
Division One Winners: Celtic
Scottish Cup Winners: East Fife
Match Results
| Round | Competition | Date | Venue | Outcome | Opponents | For | Agt | Crowd | ||
| Division 1 | Aug | 14 | Sat | H | D | Falkirk | 0 | 0 | 20,000 | |
| Division 1 | 18 | Wed | H | W | Motherwell | 2 | 1 | 22,000 | ||
| Division 1 | 21 | Sat | a | D | Hibs | 0 | 0 | 31,000 | ||
| Division 1 | 25 | Wed | a | W | Falkirk | 1 | 0 | 24,000 | ||
| Division 1 | 28 | Sat | H | D | St Johnstone | 2 | 2 | 20,000 | ||
| Division 1 | Sep | 4 | Sat | a | D | Motherwell | 1 | 1 | 25,000 | |
| Division 1 | 11 | Sat | H | W | Celtic | 3 | 1 | 80,000 | ||
| Division 1 | 15 | Wed | H | W | Hibs | 2 | 0 | 12,000 | ||
| Division 1 | 18 | Sat | a | D | Ayr Utd | 1 | 1 | 16,000 | ||
| Division 1 | 25 | Sat | H | W | St Mirren | 4 | 0 | 12,000 | ||
| Division 1 | Oct | 2 | Sat | a | W | Third Lanark | 2 | 1 | 19,000 | |
| Division 1 | 9 | Sat | H | W | Dundee | 6 | 0 | 30,000 | ||
| Division 1 | 23 | Sat | H | D | Hamilton Acas | 2 | 2 | 12,000 | ||
| Division 1 | Nov | 6 | Sat | H | W | Kilmarnock | 4 | 1 | 12,000 | |
| Division 1 | 13 | Sat | a | D | Arbroath | 1 | 1 | 9,000 | ||
| Division 1 | 20 | Sat | H | W | Morton | 3 | 1 | 8,000 | ||
| Division 1 | 27 | Sat | H | L | Hearts | 0 | 3 | 51,000 | ||
| Division 1 | Dec | 4 | Sat | a | D | Clyde | 1 | 1 | 20,000 | |
| Division 1 | 11 | Sat | H | W | Queen's Park | 2 | 1 | 10,000 | ||
| Division 1 | 25 | Sat | a | W | St Johnstone | 5 | 1 | 10,000 | ||
| Division 1 | Jan | 1 | Sat | a | L | Celtic | 0 | 3 | 83,500 | |
| Division 1 | 3 | Mon | H | L | Partick Thistle | 1 | 3 | 20,000 | ||
| Division 1 | 8 | Sat | H | D | Ayr Utd | 2 | 2 | 20,000 | ||
| Division 1 | 15 | Sat | a | D | St Mirren | 1 | 1 | 20,000 | ||
| 1st | Scottish Cup | 22 | Sat | a | W | Alloa Athletic | 6 | 1 | 9,400 | |
| Division 1 | 29 | Sat | H | W | Third Lanark | 3 | 0 | 12,000 | ||
| Division 1 | Feb | 5 | Sat | a | L | Dundee | 1 | 6 | 12,000 | |
| 2nd | Scottish Cup | 12 | Sat | H | W | Queen of the South | 3 | 1 | 50,000 | |
| Division 1 | 19 | Sat | a | D | Hamilton Acas | 2 | 2 | |||
| Division 1 | 26 | Sat | H | D | Aberdeen | 2 | 2 | 35,000 | ||
| Division 1 | Mar | 5 | Sat | a | W | Queen of the South | 2 | 0 | ||
| Division 1 | 12 | Sat | a | L | Kilmarnock | 1 | 2 | 25,000 | ||
| Quarter | Scottish Cup | 19 | Sat | a | W | Falkirk | 2 | 1 | 20,058 | |
| Division 1 | 23 | Wed | H | W | Arbroath | 3 | 1 | |||
| Division 1 | 26 | Sat | a | W | Morton | 3 | 2 | 8,000 | ||
| Semi | Scottish Cup | Apr | 2 | Sat | n | L | Kilmarnock | 3 | 4 | 70,833 |
| Division 1 | 9 | Sat | H | W | Clyde | 1 | 0 | 7,000 | ||
| Division 1 | 13 | Wed | a | W | Aberdeen | 3 | 0 | 18,000 | ||
| Division 1 | 16 | Sat | a | W | Queen's Park | 3 | 0 | 20,000 | ||
| Division 1 | 18 | Mon | a | D | Partick Thistle | 1 | 1 | 20,000 | ||
| Division 1 | 23 | Sat | a | L | Hearts | 2 | 3 | 25,000 | ||
| Division 1 | 30 | Sat | H | L | Queen of the South | 2 | 3 | 12,000 |
