With the continuous development of deep learning, neural networks have made great progress in license plate recognition (LPR). Nevertheless, there is still room to improve the performance of license plate recognition for low-resolution and relatively blurry images in remote surveillance scenarios. When it is difficult to enhance the recognition algorithm, we choose super-resolution (SR) to improve the quality of license plate images and thereby provide clearer input for the subsequent recognition stage. In this paper, we propose an automatic super-resolution license plate recognition (SRLPR) network which consists of four parts separately: license plate detection, character detection, single character super-resolution, and recognition. In the training stage, firstly, LP detection model needs to be trained alone and then its detection results will be used to successively train the three subsequent modules. During the test phase, for each input image, the network can get its LP number automatically. We also collect an applicable and challenging LPR dataset called SRLP, which is collected from real remote traffic surveillance. The experimental results demonstrate that our method achieves comprehensive quality of SR images and higher recognition accuracy compared with state-of-the-art methods. The SRLP dataset and the code for training and testing SRLPR network are available at https://pan.baidu.com/s/1vnhRa-c-dBj6jlfBZV5w4g.