To be competitive in today’s fast moving market place, organizations need to derive innovations in every part of their business. In order to accomplish the same, more and more companies are embracing agile development as a viable development methodology that delivers customer value faster with IT and cross key business units. Effort estimation is one of the key features for the success of the projects. As effort estimation is the biggest challenge in agile based projects because of the volatile nature of the requirements, so there is a need for efficient techniques for better results. Story point based approach is found to be a suitable metric for agile projects in spite of being relative in nature. This work has incorporated this approach to estimate the effort needed to perform regression testing. As in agile projects, the requirements keep on changing as per the need and the demand of the client which makes regression testing as an integral part of agile methodology. But in existing techniques of effort estimation, it is  not taken into account. This work proposes a technique for effort estimation of regression testing in agile software development by incorporating story points approach.