The college, which employs about 480 staff, said it had been operating with a "staff surplus" for several years which must now be addressed.
The decision "has no impact" on students, it said, and although 76 posts might go, it was anticipated the final figure "will be less than this".
UCU (University and College Union) said it had "seen it coming to some extent" but was "shocked" at the scale of it.
Read more news for Shropshire
The college said it would be offering voluntary redundancies to reduce the need for compulsory redundancies.
Interim and agency staffing would be "significantly" reduced and there would be opportunities for staff to retrain, it added.
A 30-day consultation has started to discuss the proposals.
College principal and chief executive Graham Guest said its priority was to "build on the improvements noted and highlighted by both Ofsted and the FE commissioner" during recent visits.
In its June 2016 inspection, Ofsted found the college was operating inadequately but has found improvements during two recent visits.
The college is in the process of merging with the town's New College, but said the job proposals were nothing to do with that.
It could not say if there would be further job losses when the merger takes place.
Vice chair of the college branch of UCU Crispin Barker said the union had been in communication with management and knew about the financial pressure the college was under.
Mr Barker said he was "sure" the figure of 76 would be reduced from what he had been told by the college.
The union said it intended to work with college leaders to minimise any "potential impact upon the learner experience".
More than 70 jobs are facing the axe at Telford College of Arts and Technology.