The verification of copyright and authenticity for medical images is critical in telemedical applications. Watermarking is a key technique for protecting medical images and can be mainly divided into three categories: region of interest (ROI) lossless watermarking, reversible watermarking and zerowatermarking. However, ROI lossless watermarking causes biases on diagnosis. Reversible watermarking can hardly provide a continuous verification function and may face verification disputes after image recovering. Zero-watermarking requires third-party storage which may cause additional security problems. To address these issues, a hybrid reversible-zero watermarking (HRZW) is proposed in this paper to effectively combine the complementary advantages of reversible watermarking and zero-watermarking. In our scheme, a novel hybrid structure is designed including a zero-watermarking component and a reversible watermarking component. In the first component, ownership share is generated by mapping nearest neighbor grayscale residual (NNGR) based features and watermark information. In the second component, the generated ownership share is embedded reversibly based on Slantlet Transform, Singular Value Decomposition and Quantization Index Modulation (SLT-SVD-QIM). Experimental results demonstrate that our proposed scheme not only yields remarkable watermarking imperceptibility, distinguishability and robustness, but also provides continuous verification function without any dispute or third-party storage, which outperforms existing watermarking schemes for medical images.