The finite and infinite horizon stochastic linear quadratic optimal control algorithms for discrete-time Markov jump with multiplicative and additive noise system are presented based on Bemllman stochastic dynamic programming. And an optimal control is studied when the noises are correlated. The solution to the controller boils down to solving a set of algebra Riccati equations. The algebra Riccati equations include the noise covariance matrix which describes the effect of the noise on the controller, so the performance of the system is improved. Finally, the simulation results show that the performance of the system with the controller in this paper is better than that of the nominal system.