Anaerobic digestion process is a spreading rapidly biotechnology for conversion of various organic wastes into bioenergy. This process can be modelled as a biochemical reaction kinetics. This approach is useful for analysis of the process. For this reason, efficient numerical methods are needed to solve this type of model. The main contribution of this study is to solve the biochemical reaction kinetics model for methane production from anaerobic digestion process of cellulose. This model provides a system of ordinary differential equations. For solving this system, a method is designed based on the universal approximation capability of a three layer feedforward sigmoidweighted neural networks with Adam optimization algorithm. This method is illustrated with numerical simulations. Moreover, the classical numerical methods such as Runge-Kutta method (RK45) and sigmoid neural networks are presented to show that all methods yield similar results.