Biogas production is a relatively novel and developing branch of the renewable fuel sector, which allows agricultural waste, and more, to be used as a feedstock. New technologies have been integrated into the process to improve its efficiency. In this study, a pump-mixed anaerobic digestion concept is considered for both experimental and modeling approaches. The experiment included a total of nine configurations with the same geometry (140 dm3 of total reactor volume) but different hydraulic retention times and mixing intervals. The measurements were used to create and optimize a mathematical model. The complete-stirring assumption, which underlies most anaerobic digestion (AD) simulations, is no longer valid in this case. Thus, the novel concept is developed by assuming that the liquid phase is split into three separate sections, which approximates the concentration gradient in a real reactor. This method allows partial differential equations to be avoided, which could potentially affect the calculation efficiency. The final mean accuracy of the model in the tested range was estimated to be 86.60% while, in selected parts of the scope, was close to 90%. The pump-mixed anaerobic digestion technique in the experiment achieved high production performance (above 8 dm3 of product per 1 dm3 of feedstock) while maintaining a high methane content (approximately 65%). The comparison between the reactor stirred by an impeller, and the pump-mixed, indicated that the proposed configuration ensures better production stability. Additionally, it was possible to achieve a higher biogas production rate with the same feedstock concentration.