Aiming at the unstructured characteristics of speech signal, a method of speaker authentication based on quantum tunneling effect was proposed. Based on quantum tunneling effect, the quantum properties of speech signal framing analyzed, and each speech signal frame was regarded as a quantum state, and the quantization of the algorithm was realized. And then the potential barrier was used to separate the energy characteristics. The barrier group was constructed to extract the energy spectrum characteristics of the signal and used it as the characteristic parameter. The speech signal modeling was finally carried out by the Gaussian Mixture Model (GMM) to complete the authentication of the speaker. The simulation results show that compared with the traditional method, the use of quantum tunneling theory to achieve speaker identification can reduce the complexity of algorithm effectively, improve the discrimination and provide a new direction for speaker authentication and quantum information theory.