Target decomposition features are the cornerstone of subsequent analyses for PolSAR images. Generally, adopting single or several decomposition algorithms limits the representation ability for original terrain characteristics. Using all the existing decomposition features, however, will definitely increase computational complexity. Besides, some features even have a negative effect on the following tasks. To address these problems, a sparse variational autoencoder feature selection framework (SVAE-FS) is proposed in this article. In detail, the encoder transforms the original feature set into latent space and then decoder reconstructs the corresponding pseudo set on this latent space. Similarly, a pseudo subset is subsequently obtained by the SVAE. The discrepancy, namely reconstruction error, between the pseudo set and the pseudo subset is taken as an evaluation criterion which reflects the feature representation ability of pseudo subset. Sparse constraint in the encoder makes the representative features stand out. Meanwhile, the linear feature transformation layer of the encoder enables the SVAE to evaluate different scale subsets without repeated training. Finally, a greedy selection approach with search scale K is proposed to find the suboptimal subset. This procedure not only reduces time consumption, but also ensures the performance of the subset. The selected features are analyzed on four real PolSAR datasets according to the terrain scattering characteristics. Furthermore, these features have achieved competitive performance on three PolSAR image tasks.