Graphs have become increasingly important in modeling structures with broad applications like Chemical informatics, Bioinformatics, Web page retrieval and World Wide Web. Frequent graph pattern mining plays an important role in many data mining tasks to find interesting patterns from graph databases. Among different graph patterns, frequent substructures are the very basic patterns that can be discovered in a collection of graphs. We extended the problem of mining frequent subgraph patterns to the problem of mining sequential patterns in a graph database. In this paper, we introduce the concept of Sequential Graph-Pattern Mining and proposed two novel algorithms SFG(Sequential Frequent Graph Pattern Mining) and TCSFG(Top-k Closed Sequential Frequent Graph Pattern Mining). SFG generates all the frequent sequences from the graph database, whereas TCSFG generates top-k frequent closed sequences. We have applied these algorithms on synthetic graph database and generated top-k frequent graph sequences.