A lossless compression method for 3-D color images is proposed based on Improved Integer Karhunen-Loeve Transform(IIntKLT), incorporated with SPECK for color image compression. First, the IIntKLT is applied to reduce the redundancies between the color components, so that the complete reversible transform is guaranteed, and then by using SPECK, the performance of coding is improved. The results of experimentation of standard testing color image, show that the new approach has an increase of 0.1 bpp in lossless image compression, and in the case of complete reversible lossy compression, compared with JPEG2000, it at most has a increase of 0.88 dB.