With the launch of high-resolution series satellites and the development of UAV hyperspectral, the available hyperspectral data are further expanded. Hyperspectral unmixing is a crucial task to improve hyperspectral images’ fine utilization value. With the rapid development of computer and artificial intelligence technology, deep learning theory has been introduced into the image processing field. The autoencoder network has been taken into hyperspectral unmixing because of its great feature extraction ability. This study improves the autoencoder structure and proposes a deep stack autoencoder network (DSAE) for hyperspectral image unmixing. The network consists of endmember extraction (EDSAE) and abundance estimation(ADSAE). Firstly, the EDSAE network is constructed by adding batch normalization, sparse constraint, “sum-to-one” constraint and deleting the bias term. Then unsupervised training is carried out for endmember extraction. Secondly, the obtained endmember spectral data are enhanced based on the HAPKE and LINEAR models. Finally, the supervised training network ADSAE is constructed based on the original stack autoencoder network, and the activation function of the last layer is set as the Softmax function. The simulated dataset is used as a training set, and the hyperspectral images are used as a test set. Based on the DSAE method proposed in this study, end member extraction and abundance estimation are carried out on three hyperspectral images, including Samson, Jasper Ridge and Urban. The results are compared with those obtained by the traditional methods N-FINDR, VCA, MVC-NMF and other deep learning methods SNSA and EndNet. The experimental results show that theD SAE method has obvious advantages over the other five methods in endmember extraction for the three real hyperspectral data set. It also shows the best abundance estimation results based on the synthetic datasets generated by the HAPKE mixing model. The DSAE method has good stability and robustness, which provides a new idea for the quantitative analysis and utilization of hyperspectral images.