Object-oriented design patterns are frequently used in real-world applications. Detection of design patterns is essential for comprehension of the intent and design of a software project. This paper presents a graph-mining approach for detecting design patterns. Our approach is based on searching input design patterns in the space of model graph of the source code by isomorphic sub-graph search method. We developed a tool called DesPaD to apply our pattern detection approach in an automated-way. We successfully detected 23 GoF design patterns in the demo source code of the Applied Java Patterns book and also obtained encouraging results out of our experiments that we conducted on JUnit 3.8, JUnit 4.1 and Java AWT open source projects.