The increasing growth in the demand for cloud computing services, due to the increasingly digital transformation and the high elasticity of the cloud, requires more efforts to improve the electrical energy efficiency of cloud data centers. In this paper, an energy-efficient hybrid (EEH) framework for improving the efficiency of consuming electrical energy in data centers is proposed and evaluated. The proposed framework is based on both the requests' scheduling and servers' consolidation approaches rather than depending on only one approach as in existing related works. The EEH framework sorts the customers' requests (tasks) according to their time and power needs before performing the scheduling. It has a scheduling algorithm that considers power consumption when taking its scheduling decisions. It also has a consolidation algorithm that determines the underloaded servers to be slept or hibernated, the overloaded servers, the virtual machines to be migrated and the servers that will receive migrated virtual machines. In addition, the EEH framework includes a migration algorithm for transferring migrated virtual machines to new servers. Results of simulation experiments indicate the superiority of the EEH framework over approaches that depend on using only one approach to reduce power consumption in terms of Power Usage Effectiveness (PUE), Data Center Energy Productivity (DCEP), average execution time, throughput and cost-saving. Index terms-green computing, scheduling, consolidation, power consumption.