In this paper, we studied an Adaptive Nadaraya Watson kernel estimator to check the bias effect on both side of the discontinuity in the presence of jump size for regression discontinuity model. We have proposed the modified Adaptive Nadaraya Watson kernel estimator and derived its normality andvariance. We have also compared with the asymptotic normality of the Mean Integrated Square Error (MISE) of Adaptive Nadaraya Watson kernel estimator and Nadaraya Watson kernel estimator. The results obtained from the simulation study have showed that Adaptive Nadaraya Watson estimator has better performance than the Nadaraya Watson Kernel estimator.