Due to their light weight, flexibility, and low energy consumption, ionic electroactive polymers have become a hotspot for bionic soft robotics and are ideal materials for the preparation of soft actuators. Because the traditional ionic electroactive polymers, such as ionic polymer-metal composites (IPMCs), contain water ions, a soft actuator does not work properly upon the evaporation of water ions. An ionic liquid polymer gel is a new type of ionic electroactive polymer that does not contain water ions, and ionic liquids are more thermally and electrochemically stable than water. These liquids, with a low melting point and a high ionic conductivity, can be used in ionic electroactive polymer soft actuators. An ionic liquid gel (ILG), a new type of soft actuator material, was obtained by mixing 1-butyl-3-methylimidazolium tetrafluoroborate (BMIMBF4), hydroxyethyl methacrylate (HEMA), diethoxyacetophenone (DEAP) and ZrO2 and then polymerizing this mixture into a gel state under ultraviolet (UV) light irradiation. An ILG soft actuator was designed, the material preparation principle was expounded, and the design method of the soft robot mechanism was discussed. Based on nonlinear finite element theory, the deformation mechanism of the ILG actuator was deeply analyzed and the deformation of the soft robot when grabbing an object was also analyzed. A soft robot was designed with the soft actuator as the basic module. The experimental results show that the ILG soft robot has good driving performance, and the soft robot can grab a 105 mg object at an input voltage of 3.5 V.