In this paper a new technique have been introduced for image compression using Fractal characteristics. Compressing images in data storage and transformation is extremely important and valuable, for this reason researchers are always looking for different techniques to resolve this issue. In this paper we have used a combined method of estimating nearest neighbor, and with the help of an adaptive method to evaluate the Range of image sizes, a solution for compressing images is introduced which first the final image is appropriate after it is retrieved, second with respect to the selection of appropriate boundary in the blocks neighborhood along with the selection of sizes for picked blocks, the speed of algorithm execution with respect to the methods introduced, and also the quality has improved respectively. This method has been implemented in the Matlab platform on several images, and the analysis shows the improvement respective to other methods.