Manager: Bill Struth
Home: Ibrox Stadium
Scottish League Winners: Rangers
Scottish Cup Winners: Partick Thistle
Match Results
| Round | Competition | Date | Venue | Outcome | Opponents | For | Agt | Crowd | ||
| Scottish League | Aug | 17 | Tue | H | W | Airdrie | 4 | 1 | 12,000 | |
| Scottish League | 21 | Sat | H | W | Motherwell | 2 | 1 | 45,000 | ||
| Scottish League | 24 | Tue | H | W | Aberdeen | 2 | 1 | 20,000 | ||
| Scottish League | 28 | Sat | a | W | Kilmarnock | 2 | 1 | 15,000 | ||
| Scottish League | Sep | 1 | Wed | a | W | Motherwell | 2 | 0 | 25,000 | |
| Scottish League | 7 | Tue | H | W | Albion Rovers | 2 | 1 | 12,000 | ||
| Scottish League | 11 | Sat | H | W | Morton | 2 | 0 | 41,000 | ||
| Scottish League | 20 | Mon | a | W | Hearts | 4 | 0 | 30,000 | ||
| Scottish League | 25 | Sat | a | D | Aberdeen | 1 | 1 | 21,800 | ||
| Scottish League | 27 | Mon | H | W | Hibs | 1 | 0 | 20,000 | ||
| Scottish League | Oct | 2 | Sat | H | W | St Mirren | 2 | 0 | 20,000 | |
| Scottish League | 9 | Sat | a | W | Dumbarton | 5 | 2 | 10,000 | ||
| Scottish League | 16 | Sat | H | W | Partick Thistle | 3 | 0 | 30,000 | ||
| Scottish League | 23 | Sat | a | W | Celtic | 2 | 1 | 65,269 | ||
| Scottish League | 30 | Sat | H | W | Third Lanark | 2 | 1 | 25,000 | ||
| Scottish League | Nov | 6 | Sat | H | W | Dundee | 5 | 0 | 43,000 | |
| Scottish League | 13 | Sat | a | W | Clydebank (old) | 4 | 2 | 22,000 | ||
| Scottish League | 20 | Sat | H | W | Hamilton Acas | 4 | 0 | 25,000 | ||
| Scottish League | 27 | Sat | a | W | Albion Rovers | 2 | 1 | 22,000 | ||
| Scottish League | Dec | 4 | Sat | H | W | Queen's Park | 3 | 1 | 30,000 | |
| Scottish League | 11 | Sat | H | W | Falkirk | 2 | 0 | 25,000 | ||
| Scottish League | 18 | Sat | a | D | Ayr Utd | 1 | 1 | 13,000 | ||
| Scottish League | 25 | Sat | a | W | Clyde | 3 | 1 | 36,000 | ||
| Scottish League | Jan | 1 | Sat | H | L | Celtic | 0 | 2 | 69,260 | |
| Scottish League | 3 | Mon | a | W | Partick Thistle | 2 | 0 | 42,000 | ||
| Scottish League | 8 | Sat | H | W | Kilmarnock | 2 | 0 | 15,000 | ||
| Scottish League | 15 | Sat | a | W | Hamilton Acas | 1 | 0 | 20,000 | ||
| Scottish League | 22 | Sat | H | W | Dumbarton | 2 | 0 | 15,000 | ||
| Scottish League | 29 | Sat | a | W | Airdrie | 3 | 0 | 17,000 | ||
| 2nd | Scottish Cup | Feb | 5 | Sat | H | W | Morton | 2 | 0 | 67,000 |
| Scottish League | 9 | Wed | H | W | Raith Rovers | 1 | 0 | 15,000 | ||
| Scottish League | 12 | Sat | a | W | Dundee | 2 | 1 | 23,000 | ||
| 3rd | Scottish Cup | 19 | Sat | H | D | Alloa Athletic | 0 | 0 | 60,000 | |
| Replay | Scottish Cup | 26 | Sat | H | W | Alloa Athletic | 4 | 1 | 55,000 | |
| Scottish League | Mar | 2 | Wed | a | W | Falkirk | 2 | 0 | 9,000 | |
| Quarter | Scottish Cup | 5 | Sat | a | W | Dumbarton | 3 | 0 | 6,000 | |
| Scottish League | 9 | Wed | H | W | Ayr Utd | 7 | 2 | 8,000 | ||
| Scottish League | 19 | Sat | H | W | Clydebank (old) | 1 | 0 | 15,000 | ||
| Semi | Scottish Cup | 26 | Sat | n | W | Albion Rovers | 4 | 1 | 65,000 | |
| Scottish League | 28 | Mon | a | D | Queen's Park | 1 | 1 | 18,000 | ||
| Scottish League | Apr | 2 | Sat | a | D | Morton | 0 | 0 | 15,000 | |
| Scottish League | 9 | Sat | a | D | Hibs | 1 | 1 | 18,000 | ||
| Final | Scottish Cup | 16 | Sat | n | L | Partick Thistle | 0 | 1 | 28,294 | |
| Scottish League | 19 | Tue | H | W | Clyde | 3 | 1 | 10,000 | ||
| Scottish League | 21 | Thu | a | W | St Mirren | 1 | 0 | 10,000 | ||
| Scottish League | 23 | Sat | a | W | Third Lanark | 1 | 0 | 30,000 | ||
| Scottish League | 27 | Wed | H | D | Hearts | 0 | 0 | 10,000 | ||
| Scottish League | 30 | Sat | a | W | Raith Rovers | 1 | 0 | 15,000 |
Trivia
June 1920: Bill Struth became only the second manager in the club's history after the tragic death of William Wilton in a boating accident.
