One way to prevent image duplication is by applying watermarking techniques. In this work, the watermarking process is applied to medical images using the Fast Discrete Curvelet Transforms (FDCuT), Discrete Cosine Transform (DCT), and Singular Value Decomposition (SVD) methods. The medical image of the host is transformed using FDCuT so that three subbands are obtained. High Frequency (HF) subband selected for DCT and SVD applications. Meanwhile, SVD was also applied to the watermark image. The singular value on the host image is exchanged with the singular value on the watermark. Insertion of tears by exchanging singular values does not cause the quality of medical images to decrease significantly. The experimental results prove that the proposed FDCuT-DCT-SVD algorithm produces good imperceptibility. The proposed algorithm is also resistant to various types of attacks, including JPEG compression, noise enhancement attacks, filtering attacks, and other common attacks.