Fingerprint compression using sparse representation has been implemented. Dictionary has been formulated from a set of fingerprint patches. First construct dictionary based on predefined fingerprint image patches. Every finger print image is going to minimize by l0-minimization algorithm. Matching pursuit is a type of sparse approximation which involves finding the “best matching” projections of multidimensional data onto an over-complete dictionary D. Compared to general natural images, the fingerprint images have simpler structure and composed of ridges and valleys. In the local regions, they look the same. So the whole image is sliced into square and non-overlapping small patches. For these small patches, there are no problems about transformation and rotation. The size of the dictionary is not too large because the small blocks are relatively smaller. The seemingly contradictive effect is achieved in an unconventional optimization framework making use of L0 gradient minimization, which can globally control how many non-zero gradients are resulted to approximate prominent structures in a structure-sparsity-management manner. Coefficients can be quantized by Lloyd’s algorithm is finding evenly-spaced sets of points in subsets of Euclidean spaces, and partitions of these subsets into well-shaped and uniformly sized convex cells. Finally all values will be encoded using Arithmetic coding it is a form of entropy encoding used in lossless data compression. It compare favorably with existing more sophisticated algorithms, especially at high compression ratios.