In medical imaging and remote sensing, image fusion technique is a useful tool used to fuse high spatial resolution panchromatic images (PAN) with lower spatial resolution multispectral images (MS) to create a high spatial resolution multispectral of image fusion while preserving the spectral information in the multispectral image (MS).Image fusion is the process that combines information from multiple images of the samescene. The result of image fusion is a new image that retains the most desirable informationand characteristics of each input image. Now-a-days, almost all areas of medical diagnosis are impacted by the digital image processing. When an image is processed for visual interpretation, the human eye is the judge of how well a particular method works. Clinical application demanding Radiotherapy plan, for instance, often benefits from the complementary information in images of different modalities. For medical diagnosis, Magnetic Resonance Image (MRI) is a medical imaging technique used in radiology to visualize internal structures of the body in detail. MRI provides better information on soft tissue with more distortion. Whereas, Computed Tomography (CT) provides the best information on denser tissue with less distortion. Wavelet transform fusion is more formally defined by considering the wavelet transforms of the two registered input images together with the fusion rule .Then, the inverse wavelet transform is computed, and the fused image is reconstructed. The wavelets used in image fusion can be classified into three categories Orthogonal, Bi-orthogonal and A'trous' wavelet. Although these wavelets share some common properties, each wavelet has a unique image decompression and reconstruction characteristics that lead to different fusion results. Since medical images have several objects and curved shapes, it is expected that the curvelet transform would be better in their fusion. In this paper the fusion results are compared visually and statistically. The simulation results show the superiority of the curvelet transform to the wavelet transform in the fusion of digital image and MR and CT images from entropy, difference entropy, quality measure, standard deviation, PSNR.