Transient stability constrained optimal power flow（TSCOPF） suffers from the curse of dimensionality as well as unacceptable computational cost and memory consumption. A multi-step integration method is proposed to discrete the swing equations of generators. The TSCOPF model based on the three-step implicit Adams method is established. The Adams method used is with fourth order accuracy， big step size and simple structure which is easy to be implemented. In order to guaranty the robustness of the algorithm，improve the computational efficiency and reduce the memory usage， the combination of reduced-space approach with primal-dual interior point method is used to solve the problem. Numerical simulations on the five systems from 9 to 300 buses show that the proposed method can improve the computing speed to more than five times and thus make the proposed method suitable for online applications.