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This paper presents a single-instruction-multiple-data (SIMD) based implementation of the transient stability simulation on the Graphics Processing Unit (GPU). Two programming models to implement the standard method of the transient stability simulation are proposed and implemented on a single GPU. In the first model the CPU is responsible for part of the simulation, while the onerous computations were offloaded to the GPU, creating a hybrid GPU-CPU simulator. In the second model, the GPU performs all the computations, while the CPU simply monitors the flow of the simulation. The accuracy of the proposed methods are validated using the PSS/E software for several large test systems. A substantial increase in speed was observed for the GPU-based simulations.