Hyperspectral unmixing plays an important role in hyperspectral image processing and analysis. It aims to decompose mixed pixels into pure spectral signatures and their associated abundances. The hyperspectral image contains spatial information in neighborhood regions, and spectral signatures existing in the region also have high correlation. However, most autoencoder (AE) based unmixing methods are pixel-to-pixel methods and ignore these priors. It is helpful to add spectral-spatial information into unmixing methods. A recent trend to deal with this problem is to use convolutional neural networks (CNNs). Our proposed framework uses 3D-CNN based networks to jointly learn spectral-spatial priors. Moreover, previous AE-based unmixing methods use fixed spectral signatures for each pure material. In our work, we use a carefully designed decoder to cope with the endmember variability issue, and variational inference strategy is applied to add uncertainty property into endmembers. To avoid over-fitting, we use structured sparsity regularizers to the encoder networks, and ℓ2,1-loss is added to the estimated abundances to guarantee the sparseness. Experimental results on both simulated and real data demonstrate the effectiveness of our proposed method.