Cloud services have been commonly used in educational contexts. However, there are only a few studies devoted to exploring the factors that influence students' intention to use cloud services from the aspect of motivation. Motivation, including intrinsic and extrinsic ones, is one of the most important factors that drive people to expend effort in accomplishing tasks. The studies on technology acceptance regarded perceived enjoyment as the intrinsic motivation and perceived usefulness as the extrinsic motivation. Combining perceived enjoyment with perceived usefulness, that is, intrinsic and extrinsic motivations, this study developed a research model to explore the factors that influence students' intention to use cloud services. The research findings of this study indicate that (1) both intrinsic and extrinsic motivations were driven by the ease of use of cloud services, in which intrinsic motivation has a higher susceptibility; (2) intrinsic motivation directly influenced extrinsic motivation and behavioral intention; (3) extrinsic motivation indirectly influenced behavioral intention through attitude toward using.