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Since biometric data are unique and permanent characteristics of individuals, the privacy protection of biometric authentication schemes has become a common concern of the public. Recently, Tang et al. proposed a biometric-based authentication scheme in an attempt to solve the privacy concerns. However, their scheme cannot resist the attack of tamper. Motivated by these concerns, in this paper, we proposed a new biometric-based authentication scheme, which achieves identity privacy and transaction untraceability. Its security is based on the semantic security of the ElGamal algorithm. Analysis results show that our scheme is higher in efficiency than Tang et al. scheme does, and meanwhile, it can resist the tamper attack. It is concluded that the proposed scheme is more secure and more practical than the existing ones.