Mosquito borne diseases pose a substantial threat to public health. Vector surveillance and vector control approaches are critical to diminish the mosquito population. Quick and precise identification of mosquito species predominant in a geographic area is essential for ecological monitoring and devise effective vector control strategies in the targeted areas. There has been a growing interest in fine tuning the pretrained deep convolutional neural network models for the vision based identification of insect genera, species and gender. Transfer learning is a technique commonly applied to adapt a pre-trained model for a specific task on a different dataset especially when the new dataset has limited number of training images. In this research work, we investigate the capability of deep transfer learning to solve the multi-class classification problem of mosquito species identification. We train the pretrained deep convolutional neural networks in two transfer learning approaches: i) Feature Extraction and ii) Fine-tuning. Three state-of-the-art pretrained models including VGG-16, ResNet-50 and GoogLeNet were trained on a dataset of mobile captured images of three vector mosquito species: Aedes Aegypti , Anopheles Stephensi and Culex Quinquefasciatus. The results of the experiments show that GoogLeNet outperformed the other two models by achieving classification accuracy of 92.5% in feature extraction transfer learning and 96% with fine-tuning. Also, it was observed that fine-tuning the pretrained models improved the classification accuracy.