A memristor-based fractional order circuit derived from Chua’s topology is presented. The dynamic properties of this circuit such as phase trajectories, time evolution characteristics of state variables are analyzed through the approximation method of fractional order operator. In addition, it clearly describes the relationships between the impedance variation of the memristor and the varying mobility of the doped region of the memristor in different circuit parameters. Finally, a periodic memristor-based system driven by another chaotic memristor-based fractional order system is synchronized to chaotic state via the linear error feedback technique.