The virtual machine (VM) placement problem is a major issue in optimizing resource ulitization of cloud data centers. With the rapid development of cloud computing, efficient algorithms are needed to reduce the power consumption and save energy in data centers. Many models and algorithms are designed with a objective to minimize the number of physical machines (PMs) used in a cloud data center. In this paper, we take into account the execution time of the PM, and formulat a new optimization problem of VM placement, which aims to minimize the total execution time of the PMs. We discuss the NP-hardness of the problem, and present heuristic algorithms to solve it in both offline and online scenarios. Furthermore, we conduct experiments to evaluate the performance of the proposed algorithms and the result show that our methods are able to perform better than other commonly used algorithms.