When the predictive control system has a large response time or a non-self-balancing object system with integral element, it is necessary to increase the prediction time domain to improve the control effect. Since optimization exists in the prediction time domain, the numerical solution process may fall into a pathological state as the prediction time domain is too long. Therefore, an exponential weighted asymptotic stability optimization strategy is proposed. Firstly, the state space model is reconstructed by embedding integral function to simplify the feedback correction link, and Laguerre function is introduced to further improve the MPC execution efficiency; Then, in the predictive control design, exponential weighting is used to specify the model eigenvalue in the unit circle to ensure the stability of the model; Finally, the closed-loop asymptotic stability of long predictive time domain optimal control is achieved by modifying the weight matrix. The simulation results of single variable and multivariable systems with integral objects show that the proposed MPC algorithm can effectively avoid ill conditioned numerical solutions and improve the dynamic and steady-state performance of the system.