This paper treats the automatic position and the attitude control for the underwater vehicle staying still or moving at dead slow speed. The motion control of the underwater vehicle cruising at high speed is rather easy and now in practical use successfully, because the hydrodynamic characteristics and the dynamics of the vehicle can be assumed to be linear, which allows application of linear control system using control surfaces. But the position and the attitude keeping control of the underwater vehicle staying still or moving at dead slow speed becomes non-linear system, because the speed of all degrees of freedom becomes comparable and the acceleration or the deceleration motion must be applied using thrusters. This paper describes the linear approximation of this non-linear system, and presents a linear design method.