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Deep learning is a powerful approach for distinguishing classes of images, and there is a growing interest in applying these methods to delimit species, particularly in the identification of mosquito vectors. Visual identification of mosquito species is the foundation of mosquito-borne disease surveillance and management, but can be hindered by cryptic morphological variation in mosquito vector species complexes such as the malaria-transmitting Anopheles gambiae complex. We sought to apply Convolutional Neural Networks (CNNs) to images of mosquitoes as a proof-of-concept to determine the feasibility of automatic classification of mosquito sex, genus, species, and strains using whole-body, 2D images of mosquitoes. We introduce a library of 1, 709 images of adult mosquitoes collected from 16 colonies of mosquito vector species and strains originating from five geographic regions, with 4 cryptic species not readily distinguishable morphologically even by trained medical entomologists. We present a methodology for image processing, data augmentation, and training and validation of a CNN. Our best CNN configuration achieved high prediction accuracies of 96.96% for species identification and 98.48% for sex. Our results demonstrate that CNNs can delimit species with cryptic morphological variation, 2 strains of a single species, and specimens from a single colony stored using two different methods. We present visualizations of the CNN feature space and predictions for interpretation of our results, and we further discuss applications of our findings for future applications in malaria mosquito surveillance.