With the popularization of palmprint recognition on mobile devices, the user privacy protection has become an enormous challenge. Particularly, federal learning, a distributed learning framework, provides a potential solution for the privacy protection of biometrics recognition. Unlike traditional distributed machine learning technology, federal learning allows multiple edge devices to implement collaborative training-sharing models without direct sharing of data. Although federated learning has made some progress in palmprint recognition, it still has some shortcomings in dealing with heterogeneous data distribution and dynamic adjustment. This paper introduces a federated learning palmprint recognition framework using the FedProx algorithm, which can process heterogeneous data, and the introduction of regularization of models can effectively improve the generalization ability and performance of the model. Experiments on the XJTU HW (Xi'an Jiaotong University Unconstrained Palmprint) database and the MPD database demonstrate the effectiveness of the proposed method for privacy protection in palmprint recognition.