Analyzing frequent subgraph mining (FSM) is considered as the most important challenge to graph mining domain. Many algorithms have been proposed for this problem. The plurality of these algorithms assumes that the graph data can be handled in computer memory. Actually, FSM is a primal operation in many applications such as Social Networks or chemical components, which contains a huge number of edges and vertices. The previous algorithms give insufficient solutions for the massive data. Accordingly, MapReduce paradigm introduces a distributed solution to massive data computation. Hence, the proposed algorithm in this paper, which is called MRFSG, uses an iterative MapReduce-based framework. Moreover, MRFSG is balanced the load among the system workers and reduces dependency between the workers. Our experiments evaluate the performance of MRFSG using various of datasets. The results of experiment demonstrate that the proposed algorithm can scale well and efficiently process large graph datasets on the cloud system.