Virtual machine placement is one of the core problems of resource scheduling in cloud data center. It has an important impact on the performance, resource utilization and energy consumption of data center. In order to optimize the data center energy consumption, improve resource utilization and ensure Quality of Service (QoS), a fuzzy membership degree based virtual machine placement algorithm was proposed. Firstly, combined the overload probability of physical hosts with the fitness placement relationship between virtual machines and physical hosts, a new distance measurement method was proposed. Then, according to the fuzzy membership function, the fitness fuzzy membership matrix between virtual machines and physical hosts was calculated. Finally, with the mechanism of energy awareness, the local search was performed in the fuzzy membership matrix to obtain the optimal placement scheme of the migration virtual machines. Simulation results show that the proposed algorithm can reduce the energy consumption of cloud data center, improve resource utilization and ensure QoS.