A submerged vessel should be controlled in the following way. That is, the reference value should be reached in a minimal time interval for the depth change, while the overshoot of the depth and the trim angle of the vessel should be restricted as small as possible. For these requirements it is intended to synthesize the control system with the optimal control theory. Here two methods ore investigated by a simulation study for the model of a submerged are carrier. One of them is to construct the linear feedback optimal control system to minimize the performance index of a quadratic form by a dynamic programming, and the other is to obtain the dead beat performance using a digital controller.