This paper proposes a novel high-backdrivable parallel-link manipulator with Continuously Variable Transmission (CVT) mechanism using several shaft actuators. The backdrivability is quite important and necessary for robots working around our living space to ensure the safety of us and environment. As for such robots, using a rotational actuator with a high reduction ratio reducer which has been commonly used is not adequate to realize the high backdrivability from the viewpoint of mechanical configuration. In this study, several high-backdrivable linear shaft actuators are utilized instead of it. Furthermore, the CVT mechanism which is provided by a novel configuration of the parallel mechanism is employed effectively. Using multiple linear shaft actuators and the CVT mechanism is able to surmount a drawback of the linear shaft actuator whose output force is relatively small compared with that of commonly used geared motors. As the first step of the study, a simple 1 DOF manipulator is proposed, and its kinematic and dynamic models are given. Next, a PD type feedback control signal to regulate both the arm's angle and its force/velocity ratio simultaneously is designed. A statical relation between the end-point output force of the manipulator and the CVT mechanism is illustrated. Finally, several fundamental experiments are performed using a prototype to demonstrate the effectiveness of proposed mechanism.