Document representation is one of the most fundamental issues in information retrieval application. In this aspect, to rank a document term weighting system has crucial importance. The graph-based ranking algorithms represent documents as a graph. The weight of a vertex in the graph is calculated based on the global information of that vertex. The similarity of the subject of a document to a query can be calculated by various ways and a particular calculation provides ranking to the document. This paper introduces an effective random-walk term weighting method to rank a document by considering position of terms (vertex) within the document and information gain of terms corresponds to the whole set of documents. The experiments on standard test collections show that our approach improves the recall and precision.