With continually increasing complexities of power systems, transient stability analysis as an important task for system security operation becomes very time-consuming and thus an efficient analysis tool is urgently needed. In this paper, a spatially paralleled hybrid approach combining the high-order Taylor series algorithm and the block bordered diagonal form (BBDF) was proposed to improve the computational efficiency of power system transient stability analysis. The proposed approach only exchanged high-order derivatives of generator voltages and currents between partitioned power network subsystems and the coordinated-bus cluster based on BBDF, and enhanced the triangular factorization recursive utilization rate of admittance matrix using the Taylor series algorithm with a large integration step. Finally, the proposed spatially paralleled hybrid approach was tested in the New England 39-bus, IEEE 145-bus and an expanded 580-bus systems, and simulation results have validated the proposed approach is very effective and computationally efficient for power system transient stability analysis.