In this paper, we propose generalized moment-based estimators of the Gamma-Gamma fading distribution. Specifically, the momentbased estimators are defined by using the k-th, the (k +1)-th, the l-th, and the (l +1)-th order moments. Hence, the new moment-based estimators, which can choose lower order moments, have more degrees of freedom than existing estimators. In order to compare their performance, the normalized mean square error is taken into account. We validate, by Monte Carlo simulations, that the new moment-based estimators with lower order moments are superior to the existing estimators over various channel conditions.