A new type of soft actuator material-ionic liquid gel (ILG), which consists of HEMA, BMIMBF_{4}, and TiO_{2}, can be transformed into gel state under the irradiation of ultraviolet (UV) light. In this paper, Mooney-Rivlin hyperelastic model of finite element method is proposed for the first time to study the properties of the ILG. It has been proved that the content of TiO_{2} has a great influence on the properties of the gel, and Young's modulus of the gel increases with the increase of its content, despite of reduced tensile deformation. The results in this work show that when the TiO_{2} content is 1.0 wt%, a large tensile deformation and a strong Young's modulus can be obtained to be 325% and 7.8 kPa, respectively. The material parameters of ILG with TiO_{2} content values of 0.2 wt%, 0.5 wt%, 1.0 wt%, and 1.5 wt% are obtained, respectively, through uniaxial tensile tests, including C_{10}, C_{01}, C_{20}, C_{11}, C_{02}, C_{30}, C_{21}, C_{12}, and C_{03} elements. In this paper, the large-scaled general finite element software ANSYS is used to simulate and analyze the ILG, which is based on SOLID186 element and nonlinear hyperelastic Mooney-Rivlin model. The finite element simulation analysis based stress-strain curves are almost consistent with the experimental stress-strain curves, and hence the finite element analysis of ILG is feasible and credible. This work presents a new direction for studying the performance of soft actuator for the ILG, and also contributes to the design of soft robot actuator.