To provide a polymer having a main chain of a fluorinated alicyclic structure, which has a high Tg and which has a functional group concentration sufficient to exhibit the characteristics, and a process for its production. A fluoropolymer having repeating units formed by cyclopolymerization of a functional group-containing fluorinated diene represented by the following formula:CF2nullCR1-Q-CR2nullCH2nullnull(1)wherein each of R1 and R2 which are independent of each other, is a hydrogen atom, a fluorine atom, an alkyl group having at most 3 carbon atoms, or a fluoroalkyl group having at most 3 carbon atoms, and Q is a bivalent organic group having a functional group, and a production method which comprises subjecting the above diene to radical polymerization.