Mosquitoes are vectors of numerous deadly diseases, and mosquito classification task is vital for their control programs. To ease manual labor and time-consuming classification tasks, numerous image-based machine-learning (ML) models have been developed to classify different mosquito species. Mosquito wing-beating sounds can serve as a unique classifier for mosquito classification tasks, which can be adopted easily in field applications. The current study aims to develop a deep neural network model to identify six mosquito species of three different genera, based on their wing-beating sounds. While existing models focused on raw audios, we developed a comprehensive pre-processing step to convert raw audios into more informative Mel-spectrograms, resulting in more robust and noise-free extracted features. Our model, namely ’Wing-beating Network’ or ’WbNet’, combines the state-of-art residual neural network (ResNet) model as a baseline, with self-attention mechanism and data-augmentation technique, and outperformed other existing models. The WbNet achieved the highest performance of 89.9% and 98.9% for WINGBEATS and ABUZZ data respectively. For species of Aedes and Culex genera, our model achieved 100% precision, recall and F1-scores, whereas, for Anopheles, the WbNet reached above 95%. We also compared two existing wing-beating datasets, namely WINGBEATS and ABUZZ, and found our model does not need sophisticated audio devices, hence performed better on ABUZZ audios, captured on usual mobile devices. Overall, our model has potential to serve in mosquito monitoring and prevalence studies in mosquito eradication programs, along with potential implementation in classification tasks of insect pests or other sound-based classifications.