Abstract: In order to address the challenges posed by limited computing resources and privacy leakage in the training process of edge users' replayed voice detection system, a novel approach inspired by brain-like intelligence is proposed. This approach, based Neural Circuit Policies (NCP), leverages differential privacy to create an edge-federated replayed voice detection framework. The framework comprises three key modules: data preprocessing, node parameter update, and federated aggregation. Initially, low-frequency acoustic features are extracted to yield a more expressive representation. Subsequently, the residual structure and NCP are fused together, and a lightweight network model with closed-form continuous-time neurons is constructed to reduce the complexity of the edge model. Finally, Gaussian noise is incorporated into the privacy protection mechanism, enhancing the level of privacy security. To thoroughly assess the proposed method, a Chinese voice dataset is established using recordings from mobile devices. The simulation results show that relative to the state-of-the-art replayed voice detection methods (Residual network, Light convolutional neural network, and RawNet3), while protecting privacy, the accuracy of the edge detection model of this framework is improved by 29.66% on average, the number of floating point operations is reduced by 94.14%, and the storage space occupation is reduced by 61.43%. At the same time, the generalization performance of the framework is also verified on the ASVspoof 2019 and ASVspoof 2021 dataset.