The successful convergence of Internet of Things (IoT) technology and distributed machine learning have leveraged to realise the concept of Federated Learning (FL) with the collaborative efforts of a large number of low-powered and small-sized edge nodes. In Wireless Networks (WN), an energy-efficient transmission is a fundamental challenge since the energy resource of edge nodes is restricted.In this paper, we propose an Energy-aware Multi-Criteria Federated Learning (EaMC-FL) model for edge computing. The proposed model enables to collaboratively train a shared global model by aggregating locally trained models in selected representative edge nodes (workers). The involved workers are initially partitioned into a number of clusters with respect to the similarity of their local model parameters. At each training round a small set of representative workers is selected on the based of multi-criteria evaluation that scores each node representativeness (importance) by taking into account the trade-off among the node local model performance, consumed energy and battery lifetime. We have demonstrated through experimental results the proposed EaMC-FL model is capable of reducing the energy consumed by the edge nodes by lowering the transmitted data.