In this paper, a new type of control, called a receding horizon finite memory control (RHFMC) or a model predictive finite memory control, is proposed as an optimal output feedback control for stochastic state-space systems. Constraints such as linearity, finite memory structure, and unbiasedness from the optimal state feedback control are required in advance, and in addition, the performance criterion of quadratic cost is required. Constraints for the input and the state are not assumed in this paper. The RHFMC is obtained directly by minimizing the performance criterion for stochastic state-space systems with the previous constraints. It is shown that the RHFMC can be separated into a receding horizon control and a finite-impulse response filter. The stability of the RHFMC is investigated. The validity of the proposed RHFMC is illustrated by a numerical example.