Recently, fishing line artificial muscle has been developed and is paid much attention due to the properties such as large contraction, light weight and extremely low cost. Typical fishing line artificial muscle is made from Nylon thread and made by just twisting the polymer. In this paper, because of the structure of the actuator, such actuators may be named as coiled polymer actuators (CPAs). In this paper, a CPA is fabricated from commercial Nylon fishing line and Ni-Cr alloy (Nichrome) wire is wound around it. The CPA contracts by the Joule heat generated by applied voltage to the Nichrome wire. For designing the control system, a simple model is proposed. According to the physical principle of the actuator, two first-order transfer functions are introduced to represent the actuator model. One is a system from the input power to the temperature and the other is a system from the temperature to the deformation. From the system identification result, it is shown that the dominant dynamics is the system from the input power to the temperature. Using the developed model, position control of the voltage-driven CPA is discussed. Firstly, the static nonlinearity from the voltage to the power is eliminated. Then, a 2-DOF PID controller which includes an inversion-based feed forward controller and a PID controller are designed. In order to demonstrate the proposed controller, experimental verification is shown.