Recent years have seen great development in the field of medical imaging and telemedicine. Despite the developments in storage and communication technologies, compression of medical data remains challenging. This paper proposes an efficient medical image compression method for telemedicine. The proposed method takes advantage of Radon transform whose basis functions are effective in representing the directional information. The periodic re-ordering of the elements of Radon projections requires minimal interpolation and preserves all of the original image pixel intensities. The dimension-reducing property allows the conversion of 2D processing task to a set of simple 1D task independently on each of the projections. The resultant Radon coefficients are then encoded using set partitioning in hierarchical trees (SPIHT) encoder. Experimental results obtained on a set of medical images demonstrate that the proposed method provides competing performance compared with conventional and state-of-the art compression methods in terms of compression ratio, peak signal-to-noise ratio (PSNR), and computational time.