Deep nonnegative matrix factorization (DNMF) is a promising approach for analyzing image data at hierarchical levels, as it can reveal hierarchical nonnegative features of the data in the image pattern space. Nevertheless, most existing DNMF models are unsupervised learning methods, making the image data fall in the same cone spanned by the basis images. This limitation potentially degrades the performance of the DNMF algorithms. To overcome the same cone problem, this paper proposes a novel deep-supervised cone-based NMF (DSCNMF) method. The DSCNMF model is established according to the fact that samples from the same class are confined within the same cone, whereas data from distinct classes occupy separate cones. The optimization objective of DSCNMF seeks to minimize the volume of each cone while maximizing the distance between different cones. Furthermore, graph regularization is integrated into the proposed model to preserve the local data structure. The multiplicative update formulas are acquired using the gradient descent method, and the DSCNMF algorithm is theoretically proven to be convergent. The experimental results conducted on two publicly available facial image datasets demonstrate the effectiveness and superiority of the proposed DSCNMF method compared with several state-of-the-art DNMF algorithms.