To meet the ever-increasing requirements of the applications, cloud service providers have further built and managed multiple cloud data centers in multiple regions across geographies with many physical machines (PMs). However, most of the existing resource allocation algorithms are developed for a single cloud data center, which normally cannot efficiently handle the load burst occasions where a single cloud data center may not be enough to satisfy the demands burst of applications. Therefore, it is necessary to consider how to efficiently manage multiple cloud data centers while meeting application requirements and reducing energy consumption. This paper first systematically analyzes multiple cloud data centers and energy consumption models.Then, an energy-efficient method of Resource Allocation based on Request Prediction in multiple cloud data centers (RARP) is proposed. The RARP method constructs a resource allocation framework based on request prediction in multiple cloud data centers, which anticipates the application request volume in advance. At the same time, the RARP method allocates VMs and PMs based on the principle of minimum remaining resources available to achieve minimum usage of PMs, thus minimizing energy consumption to complete application requests. Extensive experiments are conducted on the proposed RARP method through the simulation platform CloudSim. Finally, the experimental test results show that the accuracy of request detection and the energy consumption of cloud data centers are significantly better than those of the comparison algorithms.