The C-band synthetic aperture radar (SAR) observation is one of the most popular sources for high-resolution tropical cyclone (TC) wind speed estimation. The scarcity of high wind speed data with good quality restricts the inversion accuracy of high wind speed. It is a challenge to obtain a high-precision wind speed inversion model with sparse data points. In this paper, the TC wind speed is successfully estimated from the dual-polarization SAR signal. Firstly, the training dataset with a total of 327 data points is formed using the Sentinel-1A EW/IW mode images and their temporal-spatial matched Stepped Frequency Microwave Radiometer (SFMR) measurements. Then, a novel nonparametric TC wind speed estimation model (hereafter NWSE model) is proposed with this dataset by using the Bayesian nonparametric general regression method. The wind speed is interpreted as a function of the cross-polarized normalized radar cross-sections (VH-NRCS) and incident angle for the NWSE model. Moreover, the wind speed obtained from the co-polarized signal is used to improve the accuracy of NWSE model under low wind speed. Finally, the validation results show the excellent overall consistency between the model retrieved wind speed and the collocated SFMR and SMAP measurements. Specifically, considering all the wind speeds, the overall root-mean-square error and absolute bias of NWSE model are 2.85 m/s and 2.26 m/s compared with the SMAP wind speed. When considering the wind speeds larger than 30 m/s, the RMSE and bias of NWSE model are 3.75 m/s and 2.78 m/s, respectively.