Optimal control of biogas plants is a complex and challenging task due to the nonlinearity of the anaerobic digestion process involved in the conversion of biodegradable input material to biogas (a mixture of the energy carrier methane and carbon dioxide). In this paper a nonlinear model predictive control (NMPC) algorithm is developed to optimally control the substrate feed of the anaerobic digestion process on biogas plants. The implemented algorithm is investigated in a simulation study using a validated simulation model of a full-scale biogas plant with an electrical power of 750 kW, where the control objective is to achieve high biogas production and quality while maintaining stable plant operation. Results are presented demonstrating the feasibility of the proposed approach. The optimal operating state identified by the controller provides an additional return of investment of 650 €/day compared to a nominal operating state. Using the proposed algorithm it will be possible in the near future to optimize full-scale biogas plants using nonlinear model predictive control and therefore to advance the use of anaerobic digestion for eco-friendly energy production.