This paper addresses typhoon identification and positioning by using the thermal infrared data acquired by the Advanced Geostationary Radiation Imager (AGRI) on the Chinese Fengyun 4A (FY-4A) satellite. First, a training dataset, a validation dataset, and a test dataset of typhoons in the West Pacific Ocean close to China are created from the FY-4A AGRI thermal infrared data. Then, the YOLOX neural network is configured and trained, in which an average precision (AP) of 33.2 is obtained for the test dataset. Finally, with the prior knowledge that the brightness temperature of the typhoon eye is higher than that of its surroundings, the typhoon eyes are located using the morphological image processing method. The results of typhoon eye positioning are generally consistent with the Optimal Path (OP) dataset of tropical cyclones created by the China Meteorology Administration (CMA), and the mean errors in latitude and longitude are 0.0391° and 0.0334°, respectively.