In panel data, estimation is a popular point, researchers used many techniques to face the estimation in panel data; such as Generalized Least Square (GLS) technique which had been used by Swamy [13], and Generalized Method of Moment (GMM) had been used by Hansen [7] and Verbeek [15]. GLS is a technique for estimating the unknown parameters in the linear regression model. It can use in situations where Ordinary Least Squares (OLS) is statistically inefficient, or gives misleading inferences. Whereas GMM method is a very general statistical technique obtaining estimates of parameters of statistics models; many estimators are known as special cases of GMM, such as OLS, Instrumental Variables (IV) and 2 Stage Least Squares (2SLS). The present work is concerned to derive GMM for Swamy model to obtain a new estimator and variance.