Healthcare systems worldwide are burdened by mosquitoes transmitting dangerous diseases. Conventional mosquito surveillance methods to alleviate these diseases are based on expert entomologists' manual examination of the morphological characteristics, which is time-consuming and unscalable. The lack of professional experts brings a high necessity for cheap and accurate automated alternatives for mosquito classification. This paper proposes an end-to-end deep Convolutional Neural Network (CNN) for mosquito species classification by taking advantage of both dropout layers and transfer learning to enhance the performance accuracy. Dropout layers randomly disable the neurons of the neural network, mitigating co-adaptation and data overfitting. Transfer learning efficiently applies the extracted features from one dataset to others.Furthermore, a Region of Interest (ROI) visualization component is adopted to gain insight into the model learning. The generalization ability and feasibility of the proposed model are validated on four publicly available mosquito datasets. Experimental results on these datasets with an accuracy of 98.82%, 98.92%, 94.66%, and 98.40% demonstrate the superiority of our proposed system over the recent state-of-the-art approaches. The effectiveness of different numbers of dropout layers, their positions in the network, and their values are all investigated through ablation studies. Visualizing the model attention confirms that useful mosquito features are learned from insect legs and thorax through our model leading to optimistic predictions.