Singer voice classification is a meaningful task in the digital era. With a huge number of songs today, identifying a singer is very helpful for music information retrieval, music properties indexing, and so on. In this paper, we propose a new method to identify the singer's name based on analysis of Vietnamese popular music. We employ the use of vocal segment detection and singing voice separation as the pre-processing steps. The purpose of these steps is to extract the singer's voice from the mixture sound. In order to build a singer classifier, we propose a neural network architecture working with Mel Frequency Cepstral Coefficient as extracted input features from said vocal. To verify the accuracy of our methods, we evaluate on a dataset of 300 Vietnamese songs from 18 famous singers. We achieve an accuracy of 92.84% with 5-fold stratified cross-validation, the best result compared to other methods on the same data set.