In order to select useful features, recent graph mining techniques applies repeated mining of frequent subgraphs either by varying minimum supports or by dividing a graph database recursively. Frequent subgraph mining(FSM) is an important task for exploratory data analysis on graph data. Over the years, many algorithms have been proposed to solve this task. MapReduce is a programming paradigm for distributed computing on the Hadoop framework which allows to host big data handling applications. MapReduce is becoming the de-facto paradigm for computation on massive data, an efficient FSM algorithm on this paradigm is of huge demand. In this work, we propose a new frequent subgraph mining algorithm which uses an iterative MapReduce based framework. MapReduce-based frequent subgraph mining(FSM) technique through experiments seem to suggest that more frequent patterns efficiently than traditional methods can find them.