This paper discusses a position and attitude control problem of an underactuated satellite which uses on-off thruster mechanisms for control. Each thrusters has constant orientation relative to the satellite's body, and can generate only unilateral forces. The purpose of this paper is to clarify the control law for simultaneous position and attitude control for this type of satellite configuration. Considering the input constraints, we obtain the analytical solutions of the satellite's translational and rotational motion. Then the control procedure utilizing an invariant manifold is derived. Some numerical simulations are shown to verify the effectiveness of the proposed controller.