In this paper, we propose a novel hyperspectral unmixing technique based on deep spectral convolution networks (DSCN). Particularly, three important contributions are presented throughout this paper. First, fully-connected linear operation is replaced with spectral convolutions to extract local spectral characteristics from hyperspectral signatures with a deeper network architecture. Second, instead of batch normalization, we propose a spectral normalization layer which improves the selectivity of filters by normalizing their spectral responses. Third, we introduce two fusion configurations that produce ideal abundance maps by using the abstract representations computed from previous layers. In experiments, we use two real datasets to evaluate the performance of our method with other baseline techniques. The experimental results validate that the proposed method outperforms baselines based on Root Mean Square Error (RMSE).