This paper proposes a novel method to allocate virtual machines by statistical resource multiplexing based on the characteristics of virtual machine's peak workloads. In a cloud environment, if the peak workloads of multiple virtual machines overlap, the resource utilization of the cloud system can be significantly low when all these virtual machines enter the non-peak workload phases. If the overlap of workload peaks among virtual machines can be avoided, resource utilization will not fluctuate so much (heavily loaded during peak period and largely idle during non-peak period). Since the workload of an application usually follows a cyclic pattern, historical data can be analyzed to predict future workload. This paper models the workload characteristics of virtual machines through monitoring their peak workloads. A similarity matrix of VM's workloads is used to allocate virtual machines so that their workload peaks will not overlap. The performance study using CloudSim demonstrates that the proposed virtual machine allocation algorithm improves the CPU utilization by 8.9% to 12.4% under different workloads compared to the random allocation algorithm. The number of hosts needed by the algorithm is also reduced by 8.2% to 11.0% under the same workload requirements.