In this work, three types of machine learning algorithms are applied for synthetic aperture radar (SAR) wind retrieval in tropical cyclones (TCs), and the optimal method is confirmed. In total, 30 Sentinel-1 (S-1) images in dual-polarization (vertical–vertical [VV] and vertical–horizontal [VH] were collected during the period from 2016 to 2021, which were acquired in interferometric-wide and extra-wide modes with pixels of 10 m and 40 m, respectively. More than 100,000 sub-scenes with a spatial coverage of 3 km are extracted from these images. The dependences of variables estimated from sub-scenes, i.e., VV-polarized and VH-polarized normalized radar cross-section (NRCS), as well as the azimuthal wave cutoff wavelength, on wind speeds from the stepped-frequency microwave radiometer (SFMR) and the soil moisture active passive (SMAP) radiometer are studied, showing the linear relations between wind speed and these three parameters; however, the saturation of VV-polarized NRCS and the azimuthal wave cutoff wavelength is observed. This is the foundation of selecting input variables in machine learning algorithms. Two-thirds of the collocated dataset (20 images) are used for training the process using three machine learning algorithms, i.e., eXtreme Gradient Boosting (XGBoost), Multi-layer Perceptron, and K-Nearest Neighbor, and the coefficients are fitted after training completion through 20 images collocated with SFMR and SMAP data. Another 10 images are taken for validation up to 70 m/s, yielding a 2.53 m/s root mean square error (RMSE) with a 0.96 correlation and 0.12 scatter index (SI) using XGBoost. The result is better than the >5 m/s error achieved using the existing cross-polarized geophysical model function and the other two machine learning algorithms; moreover, the comparison between wind retrievals using XGBoost and Level-2 CyclObs products shows about 4 m/s RMSE and 0.18 SI. This suggests that the machine learning algorithm XGBoost is an effective method for inverting the TC wind field utilizing SAR measurements in dual-polarization.