As for a kind of medical images with clear texture feature, a new lossless compressive method is presented in this paper. With two main steps, the method firstly sets up the predictive model of the current pixel with its surrounding texture features, including its four color change gradients; and then measures the similarity of all pixels within the image with their predictive models so that the redundancy brought about by the similarity is removed and a higher compression ratio is obtained. The following simulation results show that the new method is much more efficient than JPEG-LS algorithm in the compression of such kinds of medical images.