In this paper we propose a new method for lossless compression of grayscale images based on predictive coding,in which qantized error is processed by quadtree coding.The predictive arithmetic makes the process of prediction quicker and easier by using fixed coefficient.And through quadtree coding method for quantized error,complicated course of decimal fraction is avoided.The whole process is easy to realize.The result of experimentation shows that the fina issue of prediction is much smaller than the entropy of original image.