The probability density function-based stochastic nonlinear model predictive control (SNMPC) is proposed to utilize full information of the posterior state distribution obtained from an estimator. Since the evolution of the probability density function is governed by the Fokker–Planck equation, the difficulty of formulating the associated closed-loop stochastic optimal control problem is first discussed. Subsequently, we introduce the discrete-time SNMPC scheme that deals with the open-loop stochastic optimal control problem. The continuity of the proposed objective function is proven by applying the semigroup perturbation theory. This continuity implies that the proposed open-loop stochastic optimal control problem is mathematically well-defined. In addition, the stability of the stationary process controlled by the proposed SNMPC is proven. The simulation results show the advantages of Fokker–Planck equation-based SNMPC over state-based control under nonlinear systems with imperfect measurements.