The probability density function (PDF) of the response of a non-linear stochastic system excited by white noise is assumed to be a linear superposition of basic functions. The Gaussian PDFs are used as the basic functions which coefficients are the reciprocal of the number of the basic functions. Gaussian closure method is a special case of the proposed method, Examples are given to show the application of the method to the systems with additive random excitations and those with both additive and multiplicative random excitations. The PDFs and moments obtained with the proposed method and conventional Gaussian closure method are compared with the exact ones. Numerical results showed some advantages of the proposed method over Gaussian closure method. INTRODUCTION