Display omitted •A hybrid AnMBR was developed to treat food waste with anti-fouling function.•About 21% of biomass attached on the carriers in the hybrid AnMBR.•Membrane fouling was largely alleviated in the hybrid AnMBR.•Thermophilic AD of food waste can maintain stability at high OLR. The thermophilic anaerobic digestion of food waste was a long-term challenge for maintaining process stability. A hybrid submerged anaerobic membrane bioreactor (AnMBR), integrating 27%(v/v) polyurethane sponge as fixed carriers were therefore investigated at (50 ± 2) °C. The organics removal efficiencies, COD mass balance, and membrane filtration performance were investigated in a 75-days continuously operated experiment. The results showed that methane production reached 0.31 L/(kg·COD) under an organic loading rate of 7.3 kg·COD/(m3·d). The low concentration of total volatile fatty acids of 247 ~ 274 mg/L and a high proportion of Methanosarcina (>97%) represented the high stability of the thermophilic process. Approximately 21% of biomass grew on the carriers in the hybrid AnMBR and induced a much lower suspended solids concentration and viscosity of bulk sludge. Noticeable lower trans-membrane pressure was consequently observed. The affecting factors identified by PCA analysis proved the advantages of the hybrid AnMBR for alleviating membrane fouling formation.