Ionic polymer–metal composites (IPMCs) constitute a new type of artificial muscle material that is commonly used in bionic soft robots and medical devices because of its small driving voltage and considerable deformation. However, IPMCs are limited by performance issues such as low output force and small operating time away from water. Silicon dioxide sulfonated graphene (SiO2-SGO) particles are often used to improve the performance of polymer membranes because of their hydrophilicity and high chemical stability. Reported here is the addition of SiO2-SGO particles prepared by in situ hydrolysis to perfluorosulfonic acid in order to improve the IPMC properties. Also, a predictive model was constructed based on a backpropagation neural network, with the SiO2-SGO doping amount and the IPMC excitation voltage in the input layer and the driving displacement in the output layer. The results show that the IPMC prepared with 1.0 wt. % doping content performed the best, with a maximum output displacement of 47.7 mm. The correlation coefficient (R2) was 0.9842 and the mean square error was 0.000 370 73, which show that the predictive model has high predictive accuracy and is suitable for predicting the performance of the SiO2-SGO-modified IPMC.