In this paper we present a novel lossless image compression method that is very simple and fast. The method uses linear prediction followed by arithmetic coding. Different prediction functions are used to estimate the intensity of image pixels. Two variants of the prediction algorithm are presented. One variant uses two different prediction functions and the other uses three different prediction functions. The position of the pixel in the image determines which prediction function is used. The method can be applied for images of any size and of high bit-depths. Standard images available in the literature are used to test the method. The compression ratios obtained with the proposed method are compared with the compression ratios obtained with the JPEG-LS and JPEG2000 methods and the results are satisfactory.