In this study, we propose an inverse optimal control based model predictive control approach. In inverse optimal control strategy, we firstly construct a stabilizing feedback control law and then search a meaningful cost functional. In that respect, we develop an alternative to solving the Riccati equation in MPC for linear time invariant system models. The control law is established with an appropriate scalar matrix which is found by using Big-Bang Big-Crunch(BB-BC) optimization algorithm. Simulations are done on a liquid level control system and the performance of the proposed method is compared with the performances of the classical model predictive, linear quadratic regulator and classical discrete time PID controller methods. The performance of the proposed controller is much better than the other controllers in respect to various criteria.