Generalized Method of Moment(GMM) is a popular estimation method to estimate model parameters in empirical financial studies. GMM is frequently applied to estimate diffusion models that are basic techniques of modern financial engineering. However, recent research showed that GMM had poor properties to estimate the parameters that pertain to the diffusion coefficient in diffusion models. This research corrects the weakness of GMM and suggests alternatives to improve the statistical properties of GMM estimators. In this study, a simulation method is adopted to compare estimation methods. Out of compared alternatives, NGMM-Y, a version of improved GMM that adopts the NLL idea of Shoji and Ozaki (1998), showed the best properties. Especially NGMM-Y estimator is superior to other versions of GMM estimators for the estimation of diffusion coefficient parameters.