In order to study the power generation characteristics of a Dielectric Elastomer Generator (DEG), a Finite Element (FE) model of the DEG under pure shear mode was established in the COMSOL Multiphysics commercial package. The model was based on the Yeoh constitutive relation of hyperelastic materials, coupled with the electrostatic force inside the generator membrane. The capacitance variation of the generator and the effect of power generation were studied. A pure shear tension apparatus was designed such that the DEG can be pre-stretched in the Y direction. Experiments to study the DEG performance under different pre-stretching conditions were carried out, and the capacitance change and power generating effect were obtained. The simulation data and the experimental results were compared and good agreement was found, therefore proving that the FE model is reliable. This study shows that, under the same tensile conditions, pre-stretching in the Y direction increases the initial capacitance and the capacitance changing rate of the DEG membrane. Hence, when the DEG was pre-stretched at λ=1, its rising voltage was 83 V, while at λ=2, its rising voltage was 252 V, thereby improving the power generation performance. The new research method of DEGs presented in this paper provides a new idea for the design of a generator prototype.