Abstract: The two-fluid model is a fundamental macroscopic model for describing gas-liquid two-phase flows. The single-pressure assumption is widely adopted because it avoids the difficulty of interface pressure closure. However, its strong non-linearity and tight two-phase coupling pose significant challenges for numerical solutions. As a mesoscopic kinetic method, the lattice Boltzmann method (LBM) exhibits significant advantages and wide applications in handling complex non-linear fluid problems; however, theoretical LBM models specifically designed for macroscopic two-fluid multiphase flows remain relatively scarce. Therefore, this paper constructs a novel mesoscopic LBM framework for solving the single-pressure two-fluid equations. This method employs two sets of distribution functions to describe the flows of the gas phase and the liquid phase separately: the zero-th order moment of the gas distribution function yields the gas volume fraction, and the zero-th order moment of the liquid distribution function yields the system pressure. The momentum exchange between the phases is coupled by constructing source terms that incorporate the effects of drag force, gravity, and pressure gradients. Through the Chapman-Enskog multi-scale analysis, the macroscopic two-fluid equations are strictly recovered from the LBM equations, and the relationship between the kinematic viscosity of the two phases and the relaxation time is explicitly provided. Numerical test cases include the step translation of gas-liquid two-phase flow in a pipe, steep gradient distribution, gravity settling separation, and U-tube flow. The results indicate that this method can accurately capture the evolution of the phase interface and the gravity separation process. It maintains a clear and stable interface under conditions of strong volume fraction discontinuities or steep gradients, without obvious non-physical oscillations, and can effectively handle the phenomena of phase disappearance and appearance. The distributions of pressure and volume fraction agree well with theoretical and literature results. The inter-phase coupling remains stable, and the entire simulation process exhibits good numerical stability.