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Network bandwidth and hardware technology are developing rapidly, resulting in the vigorous development of the Internet. A new concept, cloud computing, uses low-power hosts to achieve high reliability. Cloud computing increases the number of user applications on the Internet. However, the fault-tolerance is an important research topic in the study of distributed systems. To cope with the influence from faulty components, reaching a common agreement at the presence of faults before performing some user applications is essential. Moreover, the agreement problem is fundamental to fault tolerant distributed systems. To enhance fault tolerance, the agreement problem in a cloud-computing environment is revisited in this study. The proposed protocol, Fast Generalized Cloud Agreement (FGCA), achieves agreement on a common value among all nodes in a minimal number of message exchange rounds, and can tolerate a maximal number of allowable faulty components in a generalized cloud-computing environment.