Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)The kappa - mu distribution is a general fading model applied to predict multipath faded envelope in wireless channels, under a line-of-sight propagation condition. However, its algebraic moment-based estimator of the parameter kappa available in the literature depends on higher-order statistical moments, which impose a high penalty over the estimator efficiency. In this letter, we have proposed a new moment-based estimator of the parameter kappa, which depends on a simple average of the normalized envelope and takes advantage of lower estimation errors. We have proved that the proposed estimator is asymptotically efficient, from a practical point of view, since its normalized asymptotic variance closely attained the Cramer-Rao lower bound for the useful range of kappa. In addition, big sample size Monte Carlo simulations have revealed that the algebraic estimator is positively biased with a highly broad sample confidence region, in contrast to the almost unbiased proposed estimator with a much narrower sample confidence region. Furthermore, the proposed estimator yielded a much lower sample variance for the wide range of sample number when compared to the algebraic one.14 598601Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)CNPq [501281/2013-4]FAPESP [07-56024-4]