Power system dynamic simulations are crucial for the operation of electric power systems as they provide important information on the dynamic evolution of the system after an occurring disturbance. This paper proposes a robust, accurate and efficient parallel algorithm based on the Schur complement domain decomposition method. The algorithm provides numerical and computational acceleration of the procedure. Based on the shared-memory parallel programming model, a parallel implementation of the proposed algorithm is presented. The implementation is general, portable and scalable on inexpensive, shared-memory, multi-core machines. Two realistic test systems, a medium-scale and a large-scale, are used for performance evaluation of the proposed method.