Rangers finished third, twelve points behind Old Firm rivals Celtic who were champions.
There was the surprise signing of Northern Ireland international John McClelland from Mansfield Town.
The domestic cup competitions provided successful ground as Rangers reached both finals.
The team lost the 1982 Scottish Cup Final 4–1 to Aberdeen despite taking the lead in the match.
Rangers did win the 1981 Scottish League Cup Final by defeating Dundee United 2–1 with goals from Davie Cooper and Ian Redford.