Hysteretic behavior is an important consideration for smart electroactive polymer actuators in a wide variety of nano/micro-scale applications. We prepared an electroactive polymer actuator in the form of a microfiber, based on single-wall carbon nanotubes and polyaniline, and investigated the hysteretic characteristics of the actuator under electrical potential switching in a basic electrolyte solution. For actuation experiments, we measured the variation of the length of the carbon-nanotube-based electroactive polymer actuator, using an Aurora Scientific Inc. 300B Series muscle lever arm system, while electrical potentials ranging from 0.2 V to 0.65 V were applied. Based on the classical Preisach hysteresis model, we presented and validated a numerical model that described the hysteretic behavior of the carbon-nanotube-based electroactive polymer actuator. Inverse hysteretic behavior was also simulated using the model to demonstrate its capability to predict an input from a desired output. This numerical model of hysteresis could be an effective approach to micro-scale control of carbon-nanotube-based electroactive polymer actuators in potential applications.