In order to realize the green computing of the edge-cloud fiber-wireless networks, the cooperation between the edge servers and the cloud servers is particularly important to reduce the network energy consumption. Therefore, this paper proposes an energy-efficient workload allocation (EEWA) scheme to improve the energy efficiency by using the architecture of edge-cloud fiber-wireless networks. The feasibility of the proposed EEWA scheme was verified on our SDN testbed. We also do the simulation to obtain the optimal results for a given set of task requests. Simulation results show that our proposed EEWA scheme greatly reduces the blocking probability and the average energy consumption of task requests in edge-cloud fiber-wireless networks.