Recognition of person by means of their biometric characteristics is very popular among the society. Among this, for personal identification fingerprint recognition is an important technology due to its unique structure. Human fingerprints are rich in details called minutiae. This can be used for identification marks for fingerprint verification. Large volume of fingerprint images are collected and stored day by day from a wider range of applications. Compression of data is commanding of under certain circumstances due to large amount of data transmission and efficient memory utilization. A new and efficient fingerprint compression algorithm using sparse representation is introduced. Obtaining an over complete dictionary from a set of fingerprint patches allows us to represent them as a sparse linear combination of dictionary atoms. In the algorithm, first construct a dictionary for predefined fingerprint image patches. For a new given fingerprint images, represent its patches according to the dictionary by computing l0- minimization and then quantize and encode the coefficients and other related information using lossless coding methods. A fast Fourier filtering transformation for image post processing helped to improve the contrast ratio of the regenerated image Here, considered the effect of various factors on compression results. In Automatic Fingerprint identification System, the main feature used to match two fingerprint images are minutiae. Therefore, the difference of the minutiae between pre- and post-compression is considered in the project. The experiments illustrate that the proposed algorithm is robust to extract minutiae. From the results, we can say that the proposed system provides better PSNR and verbosity for reconstructed images. Compression using sparse provides a better compression ratio also.