The zero-watermarking methods provide a means of lossless, which was adopted to protect medical image copyright requiring high integrity. However, most existing studies have only focused on robustness and there has been little discussion about the analysis and experiment on discriminability. Therefore, this paper proposes a trusted robust zero-watermarking scheme for medical images based on Deep convolution neural network (DCNN) and the hyperchaotic encryption system. Firstly, the medical image is converted into several feature map matrices by the specific convolution layer of DCNN. Then, a stable Gram matrix is obtained by calculating the colinear correlation between different channels in feature map matrices. Finally, the Gram matrixes of the medical image and the feature map matrixes of the watermark image are fused by the trained DCNN to generate the zero-watermark. Meanwhile, we propose two feature evaluation criteria for finding differentiated eigenvalues. The eigenvalue is used as the explicit key to encrypt the generated zero-watermark by Lorenz hyperchaotic encryption, which enhances security and discriminability. The experimental results show that the proposed scheme can resist common image attacks and geometric attacks, and is distinguishable in experiments, being applicable for the copyright protection of medical images.