The rigidly-constrained pure shear dielectric elastomer actuator (PS-DEA) has become one of the critical configurations in linear soft actuator design due to its excellent uni-directional actuation performance and convenient preparation process. However, the theoretical analyses are primarily conducted by employing ideal models and lack consideration of the lateral necking deformation of PS-DEA, which has an essential impact on the performance evaluation and optimal design of PS-DEA. Therefore, in this paper, a user subroutine that describing the behavior of the electromechanical behavior of DE in terms of the Gent free-energy model is developed, and then a parametric model of the PS-DEA is established. Different combinations of actuator parameters are obtained by Latin hypercube sampling, and the actuator's performance under the parameters is simulated by the finite element method. The finite element results are taken as a sample set, and a BP neural network with three hidden layers is employed to train the samples and obtain a PS-DEA network prediction model, which is experimentally analyzed to validate its accuracy and effectiveness. The prediction model explores the influence of geometric and pre-stretching parameters on the actuator's performance and obtains the difference between the ideal theoretical and the network prediction model under various parameters. The method in this paper provides a new design methodology and theoretical basis for developing high-performance DE actuators.