Based upon iterative solution of multi parametric quadratic programming (MPQP) problem, explicit solution to model predictive control (MPC) of the constrained linear time-varying system is obtained. By using the principle of optimum and MPQP, an explicit algorithm for obtaining state feedback optimal control law of the constrained linear time-varying system is proposed. This paper shows that, for constrained linear time-varying system, both the control law for MPC and the state feedback optimal control law are time-varying piece wise linear. At the end of the paper, simulations for a vibration control of elevator's mechanical system are made.