The human activity recognition (HAR) and recommendation applications for mobile users require a privacy-aware and accurate data analysis model with lower time and lower energy consumption. The use of federated learning (FL) to develop a privacy-aware HAR model is an emerging research topic. However, the participating mobile devices in the FL process may slow down due to their limited computational resources, connectivity interruption, and limited battery life. To address these challenges, this paper proposes an energy-efficient FL method referred to as EnFed, with a case study on HAR. In EnFed, a mobile device that needs a model for an application requests its nearby devices with respect to an incentive. The nearby devices, which agree to the offered incentive, send their local model updates, i.e., updated local model parameters for that application, to the requesting device. The device, after receiving local model updates from the contributors, aggregates them to build a global model and then fits the model to its own dataset to build its own local model. The results show that using EnFed a resource-limited device obtains an accurate prediction model at lower time and lower energy consumption. The experimental results show that EnFed achieves above 95% prediction accuracy and outperforms the baselines. EnFed also reduces the response time above 90% than the cloud-only framework. The comparative study shows that EnFed outperforms the existing HAR approaches.