Federated learning (FL) in a bandwidth-limited network with energy-limited user equipments (UEs) is underexplored. In this paper, to jointly save energy consumed by the battery-limited UEs and accelerate the convergence of the global model in FL for the bandwidth-limited network, we propose the sliding differential evolution-based scheduling (SDES) policy. To this end, we first formulate an optimization that aims to minimize a weighted sum of energy consumption and model training convergence. Then, we apply the SDES with parallel differential evolution (DE) operations in several small-scale windows, to address the above proposed problem effectively. Compared with existing scheduling policies, the proposed SDES performs well in reducing energy consumption and the model convergence with lower computational complexity.