This study is aimed at improving calculation quality for IWA Anaerobic Digestion Model No.1 (ADM1) to simulate acidic failure of the methane fermentation systems and its performance recovery. The methanogen collected from digestate at a municipal wastewater treatment plant was cultivated in a lab-scale continuous reactor receiving acetate as a sole organic source. By varying the influent concentration during 400 days of operation, 6 datasets of acidification events were obtained to simulate the concentrations of acetate, VSS, pH, and the methane production rate. The ADM1 equipped with either pH sub-model or undissociated acetate sub-model could reproduce the deterioration of reactor performance in the acidic failure but totally failed to simulate the recovery in the subsequent lowered volumetric loading rate. The statistical analysis revealed both ADM1 models had relatively low correlation coefficient (Nash-Sutcliffe model efficiency coefficient (NSE)) of 0.31-0.38 although these were considerably improved from that without parameter calibration (NSE = −0.04). To cope with the mismatch, a lag phase sub-model was developed. The sub-model is composed of the remaining relative activity of the microorganism at which the inhibition peaked, and the half-saturation coefficient to express the specific length of lag phase. By adding the sub-model into the calibrated ADM1, NSE was significantly improved to 0.49-0.53.