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Cloud computing is a new cost-efficient computing paradigm in which information and computer power can be accessed from a Web browser by customers. Understanding the characteristics of computer service performance has become critical for service applications in cloud computing. For the commercial success of this new computing paradigm, the ability to deliver Quality of Services (QoS) guaranteed services is crucial. In this paper, we present an approach for studying computer service performance in cloud computing. Specifically, in an effort to deliver QoS guaranteed services in such a computing environment, we find the relationship among the maximal number of customers, the minimal service resources and the highest level of services. The obtained results provide the guidelines of computer service performance in cloud computing that would be greatly useful in the design of this new computing paradigm.