Spectral unmixing is a technique for remotely sensed image interpretation that expresses each (possibly mixed) pixel as a combination of pure spectral signatures (endmembers) and their fractional abundances. In this paper, we develop a new technique for unsupervised unmixing which is based on a deep autoencoder network (DAEN). Our newly developed DAEN consists of two parts. The first part of the network adopts stacked autoencoders (SAEs) to learn spectral signatures, so as to generate a good initialization for the unmixing process. In the second part of the network, a variational autoencoder (VAE) is employed to perform blind source separation, aimed at obtaining the endmember signatures and abundance fractions simultaneously. By taking advantage from the SAEs, the robustness of the proposed approach is remarkable as it can unmix data sets with outliers and low signal-to-noise ratio. Moreover, the multihidden layers of the VAE ensure the required constraints (nonnegativity and sum-to-one) when estimating the abundances. The effectiveness of the proposed method is evaluated using both synthetic and real hyperspectral data. When compared with other unmixing methods, the proposed approach demonstrates very competitive performance.