Model predictive control (MPC) is a powerful technique for optimizing the performance of control systems. However, the high computational demand in solving optimization problem associated with MPC in real-time is a major obstacle. Recurrent neural networks have various advantages in solving optimization problems. In this paper, we apply two recurrent neural network models for MPC based on linear and quadratic programming formulations. Both neural networks have good convergence performance and low computational complexity. A numerical example is provided to illustrate the effectiveness and efficiency of the proposed methods and show the different control behaviors of the two neural network approaches.