This paper proposes an iterative learning control (ILC) algorithm with the purpose of controling the output of a linear stochastic system presented in state space form to track a desired realizable trajectory. It is proved that the algorithm converges to the optimal one a.s. under the condition that the product input-output coupling matrices are full-column rank in addition to some assumptions on noises. No other knowledge about system matrices and covariance matrices is required. This paper proposes an iterative learning control (ILC) algorithm with the purpose of controlling the output of a linear stochastic system presented in state space form to track a desired realizable trajectory. It is proved that the algorithm converges to the optimal one as under the condition that the product input-output coupling matrices are full-column rank in addition to some assumptions on noises. No other knowledge about system matrices and covariance matrices is required.