This paper is concerned with finite horizon stabilization control for a class of discrete time stochastic systems subject to multiplicative noise and input delay. By constructing a new cost function, a complete solution to the problem of finite horizon stabilization is given for the first time based on previous work Zhang et al. (2015). It is shown that the system can be stabilized in the mean square sense with the receding horizon control (RHC) if and only if two new inequalities on the terminal weighting matrices are satisfied. Moreover, the two inequalities can be solved by using iterative algorithm. The explicit stabilizing controller is derived by solving a finite horizon optimal control problem. Simulations demonstrate the effectiveness of the proposed method.