In view of the sparsity of large-scale system of linear equations of power systems，a direct method for solving the sparse system of equations based on graphics processing units（GPUs）is proposed.In this method，the coefficient matrix of equations are partitioned by the ordering-first block bordered diagonal form（BBDF）partition method so that two levels of parallel structure are formed for solving the sparse linear equations with Blocks and Threads of GPUs in succession.The partition results are applied to the power system transient stability calculation，and the speed-up ratio performance of the method proposed is tested.The test results show that the proposed method is able to achieve a 3～4-fold speed-up ratio in currently used devices，and a prospective 7～8-fold speed-up ratio in the high-end devices.