An inherent parallel algorithm for simulating industrial power system transient characteristics is implemented. This algorithm is based on the waveform relaxation method (WRM). The component connection model (CCM) is applied to assemble the individual power system component models into an integrated system representation, among which the generator stator and network transients are taken into account. Moreover, four different schemes of the relaxation Newton iteration method can be used to solve these separated component equation sets concurrently. To demonstrate the effectiveness of the proposed algorithm, the IEEE second benchmark model system No. 2 and a practical industrial cogeneration system are selected for numerical illustrations. The satisfactory speedups with different concurrent and vectorized numerical realizations on both the Alliant FX/80 and the Convex C3840 multi-processor systems are also provided. Results obtained from these simulations indicate that this combined algorithm is suitable for detailed industrial power system transient analysis and multiprocessor parallel processing.