Methacrylic acid-methacrylonitrile-methacrylamide(MAN-MAA-MAM) copolymer was synthesized by using peroxide as initiator and methacrlic acid, methacrylonitrile and methacrylamide as main raw materials. The cycle-reaction of the MAN-MAA-MAM copolymers at high temperature and the thermal-properties of polymethacrylimide（PMI） were investigated. The results show that the cycle-reaction temperature of MAN-MAA-MAM copolymer is 160℃ and PMI is stable at 280℃ in air.