Diverse facets Of the Theory of Quantum Walks on Graph are reviewed Till now .In specific, Quantum network routing, Quantum Walk Search Algorithm, Element distinctness associated to the eigenvalues of Graphs and the use of these relation /connection in the study of Quantum walks is furthermore described. Different Researchers had contribution and put their benchmark idea Pertaining with this research concept. I furthermore try to investigate recent Application of Quantum walks, In specific the problem pertained with Graph matching i.e Matching nodes(vertices) of the Graphs. In this research paper,I consider how Continuous-time quantum walk (CTQW) can be directed to Graph-matching problems. The matching problem is abstracted using weighted(attributed) Graphs that connects vertices's of one Graph to other and Try to compute the distance b/n those Graphs Node's Beside that finding the matched nodes and the Cost related to Matching. eventually measuring the distance between two Graphs which might have different size then by using k-nearest neighbor (k-NN) method try to classifying those graph based on closest training examples in the feature space.