Using a biometric as an identity has the advantage that identities are unique if the underlying biometric is of a good quality, such as fingerprints, faces, irises, etc. However, biometric measurements are noisy and the existing identity-based systems cannot be used directly to construct this scheme. The error-tolerance property(Fuzzy) can be used to solve this problem. Based on the error-tolerance property, a new biometric identity based signature scheme is proposed. Our scheme is constructed in the standard model and achieves a strong security-full security. In addition, the security of our scheme is reduced to a generalized assumption-Computation Diffie-Hellman(CDH) assumption instead of other strong assumptions.