Biometric authentication is a very convenient and user-friendly method. The popularity of this method requires strong privacy-preserving technology to prevent the disclosure of template information. Most of the existing privacy protection technologies rely on classic encryption techniques, such as homomorphic encryption, which incur huge system overhead and cannot be popularized. To address these issues, we propose a novel biometric authentication scheme with privacy protection based on support vector machine and zero knowledge proof (BioAu–SVM+ZKP). BioAu–SVM+ZKP allows users to authenticate themselves to different service providers without disclosing any biometric template information. The evidence is generated through the zero-knowledge proof utilizing polynomial commitments. Our approach for generating a unique and repeatable biometric identifier from the user’s fingerprint image leverages the multi-classification property of SVM. Notably, our scheme not only reduces the communication overhead but also provides the privacy protection features. Besides, the communication overhead of BioAu–SVM+ZKP is constant. We have simulated the authentication scheme on the common dataset NIST, analyzed the performance and proved the security.