A novel tropical cyclone (TC) size estimation model (TC-SEM) in the western North Pacific was developed based on a convolutional neural network (CNN) using geostationary satellite infrared (IR) images. The proposed TC-SEM was tested using three CNN schemes: a single-task regression model that separately estimated the radius of maximum wind (RMW) and the radius of 34 kt wind (R34) of the TC, a multi-task regression model that estimated the RMW and R34 simultaneously, and a multi-task regression model using best-track TC intensity information. For model training, validation, and testing, 29,730, 2505, and 11,624 geostationary satellite images of the region around the center of the TC, respectively, were used, each containing four IR bands: short-wavelength IR (3.7 µm), water vapor (6.7 µm), IR1 (10.8 µm), and IR2 (12.0 µm). The results showed that the multi-task model performed better than the single-task model due to knowledge sharing and its ability to solve multiple interrelated tasks simultaneously. The inclusion of TC intensity information in the multi-task model further improved the performance of the RMW and R34 estimations, with correlations (mean absolute errors) of 0.95 (2.05 nmi) and 0.93 (9.77 nmi), respectively, which represent significant improvements over the performance of existing linear regression statistical methods. The results suggested that this CNN model using geostationary satellite images may be a powerful tool for estimating TC sizes in operational TC forecasts.