It is suggested that charges should start at 70p for one hour, as they currently do at most car parks except for those at Oakfield Street in Ystrad Mynach and The Twyn in Caerphilly.
The council has currently suspended charges at pay and display town centre car parks until at least March 31 to help businesses hit by coronavirus restrictions and support residents in “staying local” for shopping.
Charges introduced at five country parks in 2014 should also be removed to recognise health benefits to residents, it is said.
Charges would be scrapped at Bargoed Woodland park, Parc Cwm Darran, Parc Penallta, Pen-y-Fan Pond and Sirhowy Valley Country Park, where free parking is currently offered due to the coronavirus pandemic.