Online services, such as web service and stream processing, are the major workloads in modern datacenters. The variations in request arrival rates lead to the dynamic changes in the online services’ resource demands during their executions. Therefore, fast and accurate resource prediction of online services is essential to reasonable resource allocation in datacenters and guaranteeing the efficiency of service execution. However, existing resource prediction methods of online services can neither conduct the long-term accurate prediction, nor conduct the prediction with limited sample dataset and low time overhead. To this end, this paper proposes a resource prediction method of online services based on the periodic characteristic of requests, called PRP. Oriented to the periodic characteristics of online ser- vice requests, PRP adopts the autocorrelation function to recognize the changing period of the online services' resource usage. Then, based on the changing period, it divides the resource usage sample sequence and classifies the resource usage subsequences. Finally, based on the classified resource usage subsequences, it uses linear weighting to predict the resources of online services. Experimental results demonstrate that PRP outperforms the existing resource prediction methods in both the prediction accuracy and the computational efficiency.