In this paper， a discontinuous control method， intermittent control method， is proposed according to the insufficiency of traditional continuous control and synchronization of the fractional order chaotic system. Because of imperfect development of fractional order differential equation stability theory， by improving the controller， a new response system is constructed， the fractional order synchronous error system is converted into an integer order synchronous error system. Lyapunov stability theory is used to construct the V function， the sufficient condition is received for asymptotic stability of a fractional order chaotic system of intermittent control and synchronization， and the intermittent synchronization of the fractional order chaotic system is realized. In particular， a more simple and practical synchronization criterion can be obtained when periodic interval control is applied. Finally， numerical simulations are processed by taking fractional order Chen chaotic system as an example and the experimental results show that the intermittent control method can better realize the control and synchronization of fractional order chaotic system.