In this article, we propose a minimum simplex convolutional network (MiSiCNet) for deep hyperspectral unmixing. Unlike all the deep learning-based unmixing methods proposed in the literature, the proposed convolutional encoder–decoder architecture incorporates spatial information and geometrical information of the hyperspectral data in addition to the spectral information. The spatial information is incorporated using convolutional filters and implicitly applying a prior on the abundances. The geometrical information is exploited by incorporating a minimum simplex volume penalty term in the loss function for the endmember estimation. This term is beneficial when there are no pure material pixels in the data, which is often the case in real-world applications. We generated simulated datasets, where we consider two different no-pure pixel scenarios. In the first scenario, there are no pure pixels but at least two pixels on each facet of the data simplex (i.e., mixtures of two pure materials). The second scenario is a complex case with no pure pixels and only one pixel on each facet of the data simplex. In addition, we evaluate the performance of MiSiCNet in three real datasets. The experimental results confirm the robustness of the proposed method to both noise and the absence of pure pixels. In addition, MiSiCNet considerably outperforms the state-of-the-art unmixing approaches. The results are given in terms of spectral angle distance in degree for the endmember estimation and the root mean square error in percentage for the abundance estimation. MiSiCNet was implemented in Python (3.8) using PyTorch as the platform for the deep network and is available online: https://github.com/BehnoodRasti/MiSiCNet .