Federated learning (FL) provides a promising framework for enabling distributed machine learning based services without revealing users’ private data. In the scenario of wireless FL, to counter the eavesdropping attack when the parameter-server (PS, which is co-located with a base station, BS) sends the model-data to the wireless devices, we propose a secrecy driven FL via cooperative jamming, in which wireless devices cooperatively provide jamming to the eavesdropper to enhance the PS’s secure throughput based on the measure of physical layer security. We formulate a joint optimization of the PS’s downloading-transmission duration, all wireless devices’ uploading-transmission duration as a non-orthogonal multiple access cluster, each device’s local processing-rate and transmit powers for its uploading NOMA-transmission and jamming to the eavesdropper, with the objective of minimizing the overall latency for each round of FL iteration. Despite the non-convexity of the joint optimization problem, a layered algorithm is proposed to solve it. Taking into account the special feature of the optimal jamming solution, we further propose a benefit-sharing scheme, which is based on the principle of Nash bargaining solution, such that all wireless devices can benefit from reducing the FL latency via cooperative jamming in a fairness manner. Numerical results are provided to validate the effectiveness of our proposed algorithms as well as the performance advantage of our proposed secrecy driven FL via cooperative jamming. Experimental results based on the real data-sets and training models demonstrate that our scheme can reduce the latency by more than 35% compared to the case without using the jamming.