Bourne University of the Third Age hires a room in the building for its meetings but says members with mobility problems are finding there are no parking spaces outside.
The group wrote a letter to South Kesteven District Council, which owns the building and car park. It said that since three-hour restrictions were imposed at the neighbouring Burghley Centre car park in the summer people are now parking for longer at the corn exchange.
Honorary secretary Jackie Searl wrote: "The three-hour restrictions also mean that our members will have difficulty in finding any parking when they attend meetings because of the duration of the meetings."
The group meets at the corn exchange monthly on Monday afternoons and Wednesday mornings. The majority of its members are retired and many have mobility problems.
District council leader Linda Neal (Con) told a Bourne Town Council meeting on Tuesday that the corn exchange caretaker is also concerned about car parking.
She said: "We are exploring different options to see if there is anything that can be done about this.
"We do not want it to have too much of an effect on the corn exchange as it affects its viability."