If we account the constraints on the incremental acceleration as well as the incremental rate of the control input in the control system, the physical limit of the actuator can be considered and the stress of the system can be reduced.This paper deals with the design of the model predictive controller with the constraint on the incremental acceleration of the control input. The discrete time state space model of the plant is extended to the augmented model which has the incremental acceleration of the control input as the new input. The quadratic cost function, which is based on the control error and the incremental acceleration of the control input, is adopted. Constraints on the plant output, the control input, its incremental rate and acceleration are accounted. This constrained MPC problem can be solved by the quadratic programming procedure.To select the reasonable sampling period and prediction horizon, the lower bound of the settling time is derived for the proposed MPC system. Numerical examples illustrate the validity and effectiveness of the proposed method.