The probability density function (PDF) of the response of nonlinear stochastic system excited by white noise is assumed to be an exponential function of polynomial. Weight functions are used to make the FPK equation satisfied in the weak sense with the assumed PDF. Example is given to show the application of the method to non-linear systems. The PDFs obtained with the proposed method and conventional Gaussian closure method are compared with the exact ones. Numerical results showed that the PDF obtained with the proposed method are much close to the exact PDF. In some cases, even exact results can be obtained with the proposed method.