While lossy compression techniques are used for images, sound. where feature reproduction is more important than the actual data, it is necessary to use lossless compression for certain files containing data, programmes. Lossless compression techniques are not as effective as lossy ones and usually require a lot of computation for both compression and decompression. We presented a novel lossless compression techniques based on linear feedback shift registers. The advantage of this technique is that decompression is fairly simple and can be implemented without extensive computations. The decompression algorithm is also useful for implementation in hardware. In this paper we presented the details of the LFSR based algorithm. The results on various types of data such as images, sound files and text files presented and the results compared against existing lossless compression techniques.