Abstract: Studying the mechanism of phase interface snap-off during gas liquid immiscible displacement and its influencing factors have great significance in the field of enhanced oil and gas recovery such as gas driving, gas water alternation and foam driving. In this work, based on the original pseudopotential lattice Boltzmann model, we improved the fluid-fluid force scheme, added the fluid-solid force, coupled the Redlich-Kwong (RK) equation of state, and used the exact difference method (EDM) to add the external forces to the LBM framework. As well as verified the accuracy of the model by calibrating the thermodynamic consistency of the model and simulating a series of two phase systems such as testing the interfacial tension, static equilibrium contact angle and retention of the liquid phase at the corner. Based on the modified pseudopotential lattice Boltzmann model, we have carried out gas-liquid immiscible displacement simulations in a pore-throat-pore system, and the results have shown that: the snap-off phenomenon is related to the displacement pressure difference, pore-throat length ratio and pore-throat width ratio, and the snap-off phenomenon occurs only when the displacement pressure difference is within a certain range. When the displacement pressure difference is larger than the upper limit of the critical displacement pressure difference, the snap-off will be inhibited even if the snap-off condition predicted by the classical static rule has been reached; When the displacement pressure difference is less than the lower limit of the critical displacement pressure difference, it cannot overcome the "pinning" effect of the capillary tube and results in ineffective displacement. For the pore-throat structure with constant pore-throat width ratio, the displacement pressure difference range in which the snap-off phenomenon occurs increases as the pore-throat length ratio increases; For the pore-throat structure with constant pore-throat length ratio, the displacement pressure difference range in which the snap-off phenomenon occurs increases as the pore-throat width ratio decreases.