A new adaptive predictive control method is proposed to realize synchronization of fractional chaotic systems by combining adaptive control and predictive feedback control. Based on theory of fractional order Lyapunov stability， some new sufficient conditions for synchronization of fractional order chaotic systems are derived. Compared with the existing results， this method requires no prior knowledge of feedback gain， and has a fast convergence speed ， which is also is easy to implement in experiments. Finally， numerical experiments further demonstrate the effectiveness of the proposed synchronization method.