This paper focuses on the torsional motion of a torsional type fishing-line artificial muscle actuator, so to speak, Twisted Polymer Fiber (TPF) actuator. TPFs are expected as limited rotation motors or limited angle motors for mechatronic applications. Aiming to construct a gray-box model for TPF actuators, this paper derives the first-order transfer function as the model from the applied electrical power to the generated torque of an actuator. The relation from the temperature to the generated torsional torque is simply assumed as a linear function of which coefficient is the torsional rigidity. In the experiment, the validity of the obtained model is evaluated, and then the blocked torque of the TPF actuator is controlled.