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In this paper we present a new lossless image compression algorithm. To achieve the high compression speed we use a linear prediction, modified Golomb-Rice code family, and a very fast prediction error modeling method. We compare the algorithm experimentally with others for medical and natural continuous tone grayscale images of depths of up to 16 bits. Its results are especially good for big images, for natural images of high bit depths, and for noisy images. The average compression speed on Intel Xeon 3.06 GHz CPU is 47 MB/s. For big images the speed is over 60 MB/s, i.e., the algorithm needs less than 50 CPU cycles per byte of image.