Recently， a new direct method， called the adjoint gradient system method， has been proposed for computing the controlling unstable equilibrium point（CUEP） in transient stability analysis. According to this method， the CUEP of the post-fault power system can be found by computing the asymptotic equilibrium points of the adjoint gradient system which is derived from the original system. A modification to the method mentioned above is made in this paper. It is found that there exists a family of adjoint gradient systems for a nonlinear autonomous dynamic system such as a post-fault power system. These adjoint gradient systems share the same potential energy function and equilibrium points. To compute the CUEP of a post-fault power system more quickly， the appropriate adjoint gradient system， whose potential energy decreases fast， should be chosen as the integral equation， and the error control should be taken into consideration. Simulation results in the IEEE 39-bus system prove that the modified method can speed up the computing of CUEP of a post-fault power system efficiently.