A novel asynchronous parallel simulation method based on equivalence approach is proposed for transient stability simulation of power systems. In this method， the network is partitioned into several interconnected subsystems according to geographical positions， and the subsystems are equivalent each other at each simulation iteration step. Each subsystem utilizes the equivalent information from other subsystems to calculate independently. At each iteration step， a subsystem only needs the predictive equivalence and correctional equivalence of the adjacent subsystems once. Additionally， the asynchronous parallel technique is used to transmit and iterate the equivalent information among subsystems to speed up the convergence of iteration. Several cases demonstrate that the proposed method has fast calculation speed and high calculation efficiency， as well as the simulation precision accepted for engineering application. For some large-scale real systems， the real-time or super-real-time simulation will be realized.