Wide-field small aperture telescopes are widely used for optical transient observations. Detection and classification of astronomical targets in observed images are the most important and basic step. In this paper, we propose an astronomical target detection and classification framework based on deep neural networks. Our framework adopts the concept of the Faster R-CNN and uses a modified Resnet-50 as a backbone network and a feature pyramid network to extract features from images of different astronomical targets. To increase the generalization ability of our framework, we use both simulated and real observation images to train the neural network. After training, the neural network could detect and classify astronomical targets automatically. We test the performance of our framework with simulated data and find that our framework has almost the same detection ability as that of the traditional method for bright and isolated sources and our framework has two times better detection ability for dim targets, albeit all celestial objects detected by the traditional method can be classified correctly. We also use our framework to process real observation data and find that our framework can improve 25% detection ability than that of the traditional method when the threshold of our framework is 0.6. Rapid discovery of transient targets is quite important and we further propose to install our framework in embedded devices such as the Nvidia Jetson Xavier to achieve real-time astronomical targets detection and classification abilities.