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Compression is known as reducing the memory size of an image. In the process of compression, there will be a loss of data then this type of compression is called lossy compression. If there is no loss of data, then this type of compression is called lossless compression. This new fingerprint compression algorithm is based on Singular Value Decomposition in sparse representation. In the algorithm, firstly the uploaded image is divided into patches then secondly dictionary is created for each fingerprint image patch. These patches are compressed using SVD in sparse representation. Then the image is reconstructed. This is a Lossless compression. The experiment demonstrates that our algorithm is efficient compared with several competing compression techniques (JPEG, JPEG 2000, and WSQ), especially at high compression ratios.