The process of absorbing and recovering acid gas, especially CO2 or CO2 and H2S, in gas mixture with methane includes methane absorption of acid gas, desorption of rich-methane solution, gas stripping, heating to separate acid gas. The process features that propylene chiller or vacuum ammonia chiller is increased before the system ammonia cooler to increase cold replenishing amount to the system so as to solve the problem of lowered methane cooling effect and system temperature raise during desorption caused by decreased CO2 content. The said low temperature methanol washing process is suitable for gas purifying device with light material and/or heavy material.