Fuzzy extractor provides key generation from biometrics and other noisy data. The generated key is seamlessly usable for any cryptographic applications because its information entropy is sufficient for security. Biometric authentication offers natural and passwordless user authentication in various systems where fuzzy extractors can be used for biometric information security. Typically, a biometric system operates in two modes: verification and identification. However, existing fuzzy extractors does not support efficient user identification. In this paper, we propose a succinct fuzzy extractor scheme which enables efficient biometric identification as well as verification and it satisfies security requirements. We show that the proposed scheme can be easily used in both verification and identification modes. To the best of our knowledge, we propose the first fuzzy extractor based biometric identification protocol. The proposed protocol is able to identify a user with constant computational cost rather than linear-time computation by using other fuzzy extractor schemes. Biometric information security is an important concern of using biometric systems, so that we also provide security analysis of proposed schemes to show their security boundaries. The implementation shows that the performance of proposed identification protocol is constant and close to that of verification protocols.