As the coming era is that of digitized medical information, an important challenge to deal with is the storage and transmission requirements of enormous data, including color medical images. Compression is one of the indispensable techniques to solve this problem. In this work, we propose an algorithm for color medical image compression based on a biorthogonal wavelet transform CDF 9/7 coupled with SPIHT coding algorithm, of which we applied the lifting structure to improve the drawbacks of wavelet transform. In order to enhance the compression by our algorithm, we have compared the results obtained with wavelet based filters bank. Experimental results show that the proposed algorithm is superior to traditional methods in both lossy and lossless compression for all tested color images. Our algorithm provides very important PSNR and MSSIM values for color medical images.