In this study, the optimal control problem of nonlinear parabolic partial differential equations (PDEs) is investigated. Optimal control of nonlinear PDEs is an open problem with applications that include fluid, thermal, biological, and chemically-reacting systems. Model predictive control with a fast numerical solution method has been well established to solve the optimal control problem of nonlinear systems described by ordinary differential equations. In this study, we develop a design method of the model predictive control for nonlinear systems described by parabolic PDEs. Our approach is a direct infinite dimensional extension of the model predictive control method for finite-dimensional systems. The objective of this paper is to develop an efficient algorithm for numerically solving the model predictive control problem of nonlinear parabolic PDEs. The effectiveness of the proposed method is verified by numerical simulations.