Abstract: Based on the analysis of stochastic uncertainty in dynamical systems, a new type of stochastic discrete systems, named as the multiness stochastic discrete systems, is defined and then the linear quadric(LQ) optimal control problem for the systems is discussed. Firstly, the LQ optimal control laws with finite time and infinite time are proposed respectively. Secondly, the existence of the positive define matrix solution to the Riccati equation for solving the infinite-time LQ control law, the convergence of the numerical algorithm for solving the equation, and the stability of the closed-loop systems are discussed in detail. Finally, the simulation results show the effectiveness of the method proposed in this paper.