As a special auto-encoder, variational auto-encoder (VAE) is not only known as a branch of generation model, but also plays an important role in image feature extraction. Since VAE can get Gaussian distribution with different parameters from different types of inputs or with approximately the same parameters from the same type of input, the latent variables have obvious differences between different categories. This paper put forward a supervised variational auto-encoder (SVAE) to study the representation ability for synthetic aperture radar change detection. Firstly, the difference image is obtained by log ratio method from two original images preprocessed. Then fuzzy c-means (FCM) clustering is used to analyze difference image with the aim of acquiring pseudo labels. As for the inputs of the SVAE, they are selected directly from two SAR images instead of sampling from difference image (DI). Having the inputs and pseudo labels, SAVE can learn latent Gaussian representations according to which SVAE can make a classification for change detection (CD). Experiments on four data set demonstrate that SVAE can obtain discriminative features for CD and outperforms some related approaches.