This article studies a fast calculation method for the state failure time of nonlinear dynamic systems given the failure state set. Firstly, a classic method for global analysis of nonlinear dynamical systems, the point mapping under cell reference method, is improved to calculate the state failure time. Then the improved method is used to calculate Duffing system, a forced bistable structure, and spring loaded inverted pendulum model. The influence of the convergence threshold of the method on the calculation error and time is analyzed. The results show that the proposed method can achieve efficient calculation of failure time of a large number of state points while meeting certain accuracy requirements.