Design Patterns are proven solution to common recurring design problems. Design Pattern Detection is most important activity that may support a lot to re-engineering process and thus gives significant information to the designer. Knowledge of design pattern exists in the system design improves the program understanding and software maintenance. Therefore, an automatic and reliable design pattern discovery is required. Graph theoretic approaches have been used for design pattern detection in past. Here we are applying an algorithm for graph matching which is based on the sub graph isomorphism. The same algorithm we are here using for design pattern detection from the system design.