The ionic liquid gel (ILG), a new type of soft actuator material, is a mixture of 1-butyl-3-methylimidazolium tetrafluoroborate (BMIMBF4), hydroxyethyl methacrylate (HEMA), diethoxyacetophenone (DEAP), and ZrO2 polymerized into a gel state under ultraviolet (UV) light irradiation. The soft actuator structure consists of a layer of ionic liquid polymer gel sandwiched between two layers of activated carbon capped with gold foil. The volume of the cationic BMIM+ in the ionic liquid BMIMBF4 is much larger than that of the anionic BF4−. When voltages are applied to both sides of the actuator, the anions and cations move toward the anode and cathode of the electrode, respectively, under the electric field. The volume of the ILG cathode side therefore expands, and the volume of the ILG anode side shrinks, hence bending the entire actuator toward the anode side. The Ogden model was selected as the hyperelastic constitutive model to study the mechanical properties of the ILG by nonlinear analysis. As the ILG is an ideal material for the preparation of a supercapacitor, the equivalent circuit of the ILG can be modeled by the supercapacitor theory to identify the transfer function of the soft actuator. The central pattern generator (CPG) control is widely used in the area of biology, and CPGs based on bioinspired control methods have attracted great attention from researchers worldwide. After the continuum soft actuator is discretized, the CPG-based bioinspired method can be used to control the soft robot drivers. According to the simulation analysis results, the soft actuator can be smooth enough to reach the specified location.