With the wide spread of cloud computing technologies, we assume that increasing amount of attentions will be given to the area of software evolution processes in the context of cloud computing environments. Some major problems we are here facing now include: What kind of process a software evolution model under the circumstances of cloud computing must possess? What properties a software process must have as an attribute in order to effectively support the software evolution? How to modeling a process in the context of software evolution? While aiming to solve these mentioned problems, we focused our research on establishing a software evolution process model with independent functions as a component. In this article, the detailed discussion of our thoughts has been given and the in-depth analysis of our model is shown. Through a realistic case to which this model is applied, we concluded that our model provided the software evolution process with an effective support under the circumstances of cloud computing.