Abstract: We propose a method for BN two-phase flow containing non-conservative terms. In microscopic aspect, a GKS model which matches with the BN model is constructed. Numerical fluxes are obtained with integrating particle velocity distribution function. And non-conservative terms are explicitly introduced into evolution and construction of numerical fluxes. Non-conservative terms are well handled. This method avoids complex iterative process of Riemann solver. It has high calculation efficiency. Numerical tests show high precision.