An approximate analytical method is developed for the survival probability of a single-degree-of-freedom (SDOF) nonlinear system under the combined excitation of the deterministic harmonic and stochastic loads. Firstly, the system response of nonlinear oscillator is decomposed into the form of the sum of the deterministic periodic and the zero-mean stochastic components. Next the original nonlinear motion equation is transformed into a set of a coupled deterministic periodic component and a zero-mean stochastic component. Further, the statistical linearization method is utilized to convert the nonlinear motion equation of stochastic component into an equivalent linear form. In this regard, the Wiener path integral (WPI) method is utilized to obtain the short time transitional probability density function (PDF) of the equivalent linear equation. Finally, the survival probability of the response can be determined by integrating the short time PDF step by step through Chapman-Kolmogorov(C-K) equation. A Duffing nonlinear numerical example demonstrates the accuracy and efficiency of the developed method compared with the Monte Carlo simulation.