The massive number of users has brought severe challenges in managing cloud data centers (CDCs) composed of multi-core processor that host cloud service providers. Guaranteeing the quality of service (QoS) of multiple users as well as reducing the operating costs of CDCs are major problems that need to be solved. To solve these problems, this paper establishes a cost model based on multi-core hosts in CDCs, which comprehensively consider the hosts’ energy costs, virtual machine (VM) migration costs, and service level agreement violation (SLAV) penalty costs. To optimize the goal, we design the following solution. We employ a DAE-based filter to preprocess the VM historical workload and use an SRU-based method to predict the computing resource usage of the VMs in future periods. Based on the predicted results, we trigger VM migrations before the hosts move into the overloaded state to reduce the occurrence of SLAV. A multi-core-aware heuristic algorithm is proposed to solve the placement problem. Simulations driven by the VM real workload dataset validate the effectiveness of our proposed method. Compared with the existing baseline methods, our proposed method reduces the total operating cost by 20.9~34.4%.