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The generalized method of moments (GMM) is introduced in the framework of estimating the Nakagami-m fading parameter. This GMM approach provides a systematic procedure for finding the moment-based m parameter estimators. Using the multivariate delta method, we present a derivation for the asymptotic variance of the GMM Nakagami m parameter estimators. Monte Carlo simulation results show that the GMM approach can lead to estimators outperforming existing moment-based m parameter estimators over a wide range of channel conditions. It is shown that the asymptotic performance of these GMM estimators are close to that of the maximum-likelihood based estimator. The proposed method can be easily applied to both noiseless and noisy environments.