In recent years with the continuous growth of the demand for cloud computing the energy consumption of cloud data centers has been increasing which not only brings economic problems but also has a serious impact on the ecological environment caused by huge carbon emissions. Therefore data center energy saving has become an important problem to be solved urgently. In cloud data centers Virtual Machine Placement VMP optimization can effectively improve resource utilization. VMP is also one of the important technologies to reduce the energy consumption of data centers. Aiming at the problem of energy-aware VMP of cloud data centers an Energy-efficient Grouping Genetic Algorithm EEGGA based on grouping genetic algorithm GA was proposed. The algorithm considered the energy-efficient VMP problem as a bin packing problem BPP and applied a genetic algorithm based on grouping coding to solve it. The goal of reducing the overall energy consumption of data centers was achieved by reducing the number of active physical hosts the number of containers . At the same time several heuristic optimization strategies were designed to improve the fitness of offspring chromosomes in the crossover and mutation stages of the iteration process so as to improve the energy-saving performance of the algorithm and accelerate the speed of convergence. In the simulation experiments the proposed algorithm was compared with traditional algorithms in the aspects of convergence speed and energy-saving performance. Experimental results show that the proposed algorithm can effectively reduce energy consumption and is superior to other algorithms in terms of energy-saving performance and convergence speed.