Even though speaker recognition has gained significant progress in recent years, its performance is known to be deteriorated severely with the existence of strong background noises. Inspired by a recently proposed clean-frame selection approach, this work investigates a relatively elegant weighting method when computing the Baum-Welch statistics of Gaussian mixture models (GMMs) in i-vector extraction. By introducing weighting parameters to the frames of enrollment/testing utterances, the optimization problem is redefined and solved. New updating rules are derived by incorporating weights to the computation of posterior probabilities, mean vectors, and covariance matrices of the GMM. The experiments conducted on the Speakers in the Wild (SITW) database show that the proposed algorithm has significantly improved the performance of i-vector-based speaker recognition systems in noisy environments. Compared with the GMM i-vector baseline, the equal error rate is reduced from 5.75 to 4.72 and the minimum value of cost function (C min det) is reduced from 0.4825 to 0.4505. Slight but significant superiority is also observed over the method with an additional feature enhancement frontend by using deep neural networks. INDEX TERMS Gaussian mixture models, frame weighting, Baum-Welch statistics, i-vector, robust speaker recognition.