Background Anaerobic digestion (AD) is a suitable process for treating high moisture MSW with biogas and biofertilizer production. However, the low stability of AD performance and low methane production results from high moisture MSW due to the fast acidify of carbohydrate fermentation. The effects of organic loading and incineration fly ash addition as a pH adjustment on methane production from high moisture MSW in the single-stage AD and two-stage AD processes were investigated. Results Suitable initial organic loading of the single-stage AD process was 17 gVS L−1 at incineration fly ash (IFA) addition of 0.5% with methane yield of 287 mL CH4 g−1 VS. Suitable initial organic loading of the two-stage AD process was 43 gVS L−1 at IFA addition of 1% with hydrogen and methane yield of 47.4 ml H2 g−1 VS and 363 mL CH4 g−1 VS, respectively. The highest hydrogen and methane production of 8.7 m3 H2 ton−1 of high moisture MSW and 66.6 m3 CH4 ton−1 of high moisture MSW was achieved at organic loading of 43 gVS L−1 at IFA addition of 1% by two-stage AD process. Biogas production by the two-stage AD process enabled 18.5% higher energy recovery than single-stage AD. The 1% addition of IFA into high moisture MSW was useful for controlling pH of the two-stage AD process with enhanced biogas production between 87–92% when compared to without IFA addition. Electricity production and energy recovery from MSW using the coupled incineration with biogas production by two-stage AD process were 9,874 MJ ton−1 MSW and 89%, respectively. Conclusions The two-stage AD process with IFA addition for pH adjustment could improve biogas production from high moisture MSW, as well as reduce lag phase and enhance biodegradability efficiency. The coupled incineration process with biogas production using the two-stage AD process was suitable for the management of MSW with low area requirement, low greenhouse gas emissions, and high energy recovery.