1st Round (15 December 1979):
Annan Athletic 1-3 Stranraer
Cowdenbeath 3-0 Albion Rovers
E.Stirlingshire 1-1 Brechin City
Queen of the South 1-1 Falkirk
Spartans 1-2 Forfar Athletic
Stenhousemuir 4-2 Queen's Park

Replays 1st Round (19 Dec 1979):
Brechin City 1-1aet E.Stirlingshire
Falkirk 0-4 Queen of the South (26 Dec)
2nd Replay 1st Round (26 Dec 1979):
Brechin City 1-0 E.Stirlingshire (Muirton Park)

Bye: 10 clubs.

2nd Round (5 January 1980):
Alloa Athletic 1-0 East Fife (9 Jan)
Brechin City 1-1 Montrose (7 Jan)
Buckie Thistle 0-0 Brora Rangers
Coldstream 1-1 Queen of the South (12 Jan)
Cowdenbeath 3-2 Forfar Athletic
Stenhousemuir 0-0 Peterhead
Stranraer 1-1 Meadowbank Thistle
Threave Rovers 2-3 Keith

Replays 2nd Round (12 Jan 1980):
Brora Rangers 1-2 Buckie Thistle aet
Meadowbank Thistle 2-1 Stranraer
Montrose 3-4 Brechin City (14 Jan)
Peterhead 2-0 Stenhousemuir
Queen of the South 4-0 Coldstream (14 Jan)

Clubs from Premier (10) and First Division (14) are added.

3rd Round (26 Jan 1980):
Airdrieonians 3-1 (30 Jan) St.Johnstone
Alloa Athletic 0-1 (30 Jan) Heart of Midlothian
Arbroath 1-1 Aberdeen
Berwick Rangers 3-1 Peterhead
Celtic 2-1 Raith Rovers
Clyde 2-2 Rangers
Clydebank 1-1 Stirling Albion
Dumbarton 1-2 Ayr United
Dundee United 5-1 (30 Jan) Dundee FC
Dunfermline Athletic 2-0 (30 Jan) Buckie Thistle
Kilmarnock 0-1 (30 Jan) Partick Thistle
Hamilton Academical 2-3 Keith
Meadowbank Thistle 0-1 Hibernian
Greenock Morton 1-0 Cowdenbeath
Queen of the South 2-0 Motherwell
St Mirren 3-1 Brechin City

Replays 3rd Round (30 Jan 1980):
Aberdeen 5-0 Arbroath
Rangers - Clyde 2-0
Stirling Albion 1-1 Clydebank aet

2nd Replay 3rd Round (11 Feb 1980):
Clydebank 0-1 Stirling Albion (Brockville)

4th Round (16 February 1980):
Aberdeen 8-0 Airdrieonians
Celtic 1-1 St Mirren
Heart of Midlothian 2-0 Stirling Albion
Hibernian 2-0 Ayr United
Keith 1-2 Berwick Rangers
Greenock Morton 5-0 Dunfermline Athletic
Queen of the South 1-3 Partick Thistle
Rangers 1-0 Dundee United

Replay 4th Round (20 Feb 1980):
St Mirren 2-3 Celtic aet

Quarter Finals (8 March 1980):
Berwick Rangers 0-0 Hibernian
Celtic 2-0 Greenock Morton
Partick Thistle 1-2 Aberdeen
Rangers 6-1 Heart of Midlothian

Replay Quarter Finals (12 Mar 1980):
Hibernian 1-0 Berwick Rangers

Semi Finals (12 April 1980):
Celtic 5-0 Hibernian Hampden Park, Glasgow
Rangers - Aberdeen 1-0 Celtic Park, Glasgow

Final (Hampden Park, 10 May 1980):
Celtic 1-0 Rangers aet

Cup Winners: Celtic.