Abstarct: Fingerprint is an important physiological feature used to identify individuals Compression is a key component for storing fingerprint image using less memory. methods of compression provide easy acquiring images. One type of Wavelet transform is designed to be easily reversible. This type of wavelet transform can have used in compression. Recognition features is known vital to identity individuals. Because of these، our thesis is baxsed on wavelet transform and preserving recognition features. In order to increase recognition rate، we enhance fingerprint image by inhancing contrast in various states and SPIHT coding algorithm is used for purpose of compression fingerprint. Two method has been used for recognition. First recognition fingerprint is baxsed on miniutia extraction and other baxsed on neural network. Simulitation results in tables in form of recognition rate for different bit rate represent that first method preserved recognition rate of 0.1 bpp to high bit rates. and recognition rate for compressed fingerprint does not have a lot of different from original image. but second method with tow train image preserved recognition rate of 0.5 bpp to high bit rates. Compression test is performed on a databaxse include of fifteen fingerprint that each fingerprint have six image.