Based on the Lyapunov stability theory,the feasibility of synchronization was proved between a class of third-order memristor chaotic circuits under undirectional linear coupling. Complete synchronization can be realized when constant gain in the controller is beyond the threshold. In the case of time-varying gain in controller,synchronization still can be observed in some parameter region. Furthermore,numerical method was used to calculate the effect of gain selection in controller on the average power consumption and transient period to reach synchronization.