This paper considers the adaptive control of a class of single-input linear stochastic systems where unknown parameters in the gain vector are gaussian random variables while other unknown parameters are discrete ones. The optimal state and parameter estimator using the parallel operation of the Kalman filters are constructed and the algorithm of the suhoptimal control based on the well-known open-loop feedback optimal (OLFO) method is derived. Since the OLFO control requires extensive on-line computation, a simple suboptimal control which makes full use of the parallel structure of the estimator is proposed. The performance level and the qualitative properties of both suboptimal controls are studied by using the Monte Carlo simulation.