Abstract: An improved vector cooperative response surface method (CRSM) for structural reliability analysis involving non-Gaussian correlated random variables was proposed based on the orthogonal and approximately equivalent probability transformations. First, according to the orthogonal transformation, the non-Gaussian correlated random variables were mapped into the uncorrelated non-Gaussian standardized random variables to establish global stiffness matrices and load vectors. The preconditioner was defined by the global structure stiffness matrix to form a preconditioner Krylov subspace, and the stochastic global nodal displacement vector of structure was expanded subsequently in the subspace to develop vector cooperative response surface hierarchically. The collocation points selected from combinations of the roots of polynomial chaos of one-order higher than the order of the response surface were mapped into the non-Gaussian random variable space from the independent standard normal random variable space according to approximately equivalent probability transformation. Finally, the unknown coefficients of cooperative response surface (CRS) were determined by the regression analysis and structural reliability analysis was implemented based on the limit state function constructed by the CRS. Results show that the proposed method is of high accuracy, global applicability and fast convergence for structural reliability analysis involving non-Gaussian correlated random variables.