Inthis paper, a self-growing engine based adaptation system, which automatically decides the more efficiency plan about the assigning of jobs, in a mobile, grid computing environment, is proposed. Recently, research relating to grid computing has become an important issue, achieving certain goals by sharing the idle resources of computing devices, and overcoming various constraints of the mobile computing environment. In this domain, most existing research assigns work only by considering the status of resources. Hence the situation of assigning work to a peer having relatively low work efficiency, is possible. The proposed system considers various contexts and selects the most suitable peer. In addition, the system stores the history of the work result, and if the same request occurs in the future, a peer is selected by analyzing the history. In this paper, a prototype used to evaluate the proposed system is implemented, and the effectiveness of the system is confirmed through two experiments.