In this study, in order to liquefy methane gas, the four-stage cascade refrigeration cycle integrated with Linde-Hampson was proposed. The refrigerants R32, R23, R600, R1234yf, R141b, and R290 were used in the proposed cycle. A computer code was developed using the Engineering Equation Solver (EES-V9.172-3D). Irreversibility of the four-stage cascade refrigeration cycle integrated with Linde-Hampson was investigated according to different evaporator, condenser temperatures, and methane gas mass flow rates. As the evaporator temperature increased, the irreversibility of the cycle decreased. However, the irreversibility of the cycle increased the condenser temperature, and the mass flow rate of methane increased. The minimum amount of irreversibility of the cycle was obtained using R32 as a refrigerant, while the maximum amount of irreversibility was obtained using R23.