Receding horizon control is a type of optimal feedback control in which control performance over a finite future is optimized with a performance index that has a moving initial time and terminal time. Implicit systems belong to a more generalized class of systems than a class of explicit systems, because they can additionally contain algebraic constraints. The objective of this study is to develop a novel design method of receding horizon control for a generalized class of discrete-time nonlinear implicit systems. Using the variational principle, we derive the stationary conditions that must be satisfied for a performance index to be optimized. Moreover, we provide numerical algorithms for solving the obtained stationary conditions. Next, we establish the stability criterion for the closed-loop system with the proposed method. Finally, the effectiveness of the proposed method is verified by numerical simulations.