In this paper, a new method for the calculation of the observation-confidence value that is applied in the modified adaptive Gaussian mixture model framework is proposed for speaker verification. First, an adaptive version of the multiple low-rank representation method, for which a weighted decomposition that incorporates the prior information regarding the speech/non-speech content is considered, is proposed to find the enhanced speech and for the estimation of the frame signal-to-noise ratio (SNR) values. Then, a simple sigmoid function is applied to convert the frame SNR values into the observation-confidence values. To verify the accuracy of the system, we use utterances from the Korean movie You Came From The Stars. The experiment results show that our proposed approach achieves a greater accuracy compared with the other well-known baseline methods, such as the GMM-based universal background model, the GMM supervector-based support vector machine (SVM), the i-vector-based SVM, and the sparse representation, under the noisy environment.