In this paper, we propose a deep auto-encoder network for the unmixing for hyperspectral data with outliers and low signal to noise ratio. The proposed deep auto-encoder network composes of two parts. The first part of the network adopts stacked non-negative sparse auto-encoder to learn the spectral signatures such that to generate a good initialization for the network. In the second part of the network, a variational auto-encoder is employed to perform unmixing, aiming at the endmember signatures and abundance fractions. The effectiveness of the proposed method is verified by using a synthetic data set. In our comparison with other state-of-the-art unmixing methods, the proposed approach demonstrates highly competitive performance.