Transient stability analysis of stochastic power system with Monte Carlo simulations demands vast calculation tasks. A novel transient stability analysis method for stochastic power system based on quasi-Hamiltonian system stochastic averaging and EEAC combined method was proposed in this paper. Firstly, the stochastic power system was equivalent with a two-machine system. The stochastic differential algebraic equations model of the equivalent system was established. The transient energy of the corresponding Hamiltonian system was derived. The security region of the system was determined by the critical transient energy. Then, the stochastic averaging method was applied to analyze the quasi-Hamiltonian system. The averaged system and averaged equations were got. The diffusion process of the power system transient energy is studied by the diffusion equation theory. The conditional reliability function was governed by the backward Kolmogorov equation. The impacts of excitation amplitude, fault type and fault clearing time on transient stability can be investigated quantitatively. This method was applied in the four-generator and two-area system to verify its effectiveness. Simulations show that the results coincide with the Monte Carlo method well.