A novel fluorine-containing polymer, poly[N-(2,3,4,5,6-pentafluorophenyl) maleimide], was prepared by the anionic polymerization of N-(2,3,4,5,6-pentafluorophenyl)maleimide (PFPMI). Anionic polymerization with alkali metal tert-butoxides gave poly(PFPMI) in 14-32% yield. Phenyllithium and sec-butyllithium also afforded poly(PFPMI). No polymer was obtained with a radical initiator such as 2,2'-azoisobutyronitrile. The polymerization took place only via the vinylene group of PFPMI and no appreciable side-reaction occurred. The obtained poly(PFPMI) shows unimodal molecular weight distribution and begins to decompose at 325 degrees C.