A soft robot is composed of soft materials, which exhibit continuous deformation and driving structure integration and can arbitrarily change shapes and sizes over wide ranges. It shows strong adaptability to unstructured environments and has broad application prospects in military reconnaissance, medical rescues, agricultural production, etc. Soft robots based on ionic electroactive polymers (EAPs) have low-driving voltages, large-actuation displacements, fast responses, light weights, and low powers and have become a hot research field of bionic robots. Ionic liquid gels (ILGs) are new ionic EAPs. In this study, a new soft actuator was designed based on an ILG, and the electromechanical coupling model of an ILG soft actuator was studied in detail. Based on the system transfer function method, a mechatronic coupling model for the soft actuator was developed. According to the material characteristics and current response law of the ILG-containing EAP, an equivalent circuit model was used to describe transfer of the output current and input voltage. Based on the equivalent transformer model for ionic polymer–metal composite (IPMC) actuators proposed by Claudia Bonomo, the electromechanical coupling equation and a driving equation of the ILG soft actuator were established. The least-squares method was used with the coupling model of an ILG soft actuator to identify the system parameters for the model, and the effects of the structural parameters on the end displacement and driving force of the soft actuator were analyzed.