Anaerobic digestion (AD) is used to produce usable methane (biogas, known as methane after purification). Organic waste (or products from energy crops, solid or liquid) can thus be recovered in the form of energy. Estimating the specific growth rate of microorganisms of this process remains a difficult task. In the present study, an estimation approach of the specific growth rate of AD is proposed. First, the reduction of the anaerobic digestion model No 1 (ADM1) into a one-step model is determined from experimental data. In a second step, the estimation of the growth rate is performed using a differential algebraic approach. The estimation procedure is evaluated and its performance is highlighted through results obtained in simulation.