The performance and microbial community structure for treating lipids-rich kitchen waste slurry in mesophilic Anaerobic Membrane Bioreactor (m-AnMBR) and thermophilic AnMBR (t-AnMBR) were compared in this study. Higher Organic Loading Rate (OLR) of 12 kg-COD/(m3·d), better Chemical Oxygen Demand (COD) removal efficiency over 98%, stronger stability with Volatile Fatty Acids (VFAs)/alkalinity below 0.04, higher flux with 18 L/(m2·h) and lower Long Chain Fatty Acids (LCFAs) concentration of 550 mg/L were obtained in the m-AnMBR. Directly increasing temperature from 39 to 55 °C resulted in a collapse of the t-AnMBR. Acclimation via gradually increasing temperature made the t-AnMBR run successfully with lower OLR and COD removal efficiency of 7.5 kg-COD/(m3·d) and 96%. An obvious discrepancy of microbial community structure was presented between the m-AnMBR and t-AnMBR via the 16S rRNA gene sequence analysis. The Methanomethylovorans and Methanoculleus were dominant in the t-AnMBR instead of Methanobacterium and Methanothrix in the m-AnMBR.