Breakthrough pressure of CH4 is an important parameter in shale gas exploitation and the evaluation of cap rocks. To date, many studies have been carried out to investigate CH4 breakthrough pressure based on experimental methods, meanwhile, some studies have also proposed numerical simulation theories on multiphase flow in porous media. However, there are few studies on numerical simulation methods for predicting CH4 breakthrough pressure on rock-core scale under various conditions. Therefore, in this study, we propose a numerical method that can be used to predict CH4 breakthrough pressure in partially saturated low-permeability rock sample under multiple P-T conditions based on our published experimental results. The simulative results show that both CH4 breakthrough pressure and breakthrough time are exponentially related to temperature and pressure conditions, moreover, CH4 breakthrough pressure and breakthrough time decrease with increasing temperature and pressure. Under the multiple P-T conditions in this study, the effect of pressure on numerical results is greater than that of temperature. By comparing the numerical results with the published experimental data, it has been validated that the numerical method proposed in this study is reasonable. Furthermore, we have parametrically swept 3 key properties in CH4-H2O-rock systems, namely, dynamic viscosity, density, and interfacial tension; the order of the effects of 3 properties on the CH4 breakthrough process is, dynamic viscosity > interfacial tension > density. The numerical method established in this study can provide an important reference for the prediction of gas breakthrough process in rock core and for related numerical studies and engineering practice.