TerraSAR-X (TS-X) is a new, fully polarized X-band synthetic aperture radar (SAR) satellite, which is a successor of the Spaceborne Imaging Radar X-band Synthetic Aperture Radar (SIR-X-SAR) and the SRTM. TS-X has provided high-quality image products over land and oceans for scientific and commercial users since its launch in June 2007. In this article, a new geophysical model function (GMF) is presented to retrieve sea surface wind speeds at a height of 10 m (U 10) based on TS-X data obtained with VV polarization in the ScanSAR, StripMap and Spotlight modes. The X-band GMF was validated by comparing the retrieved wind speeds from the TS-X data with in situ observations, the high-resolution limited area model (HIRLAM) and QuikSCAT scatterometer measurements. The bias and root mean square (RMS) values were 0.03 and 2.33 m s−1, respectively, when compared with the co-located wind measurements derived from QuikSCAT. To apply the newly developed GMF to the TS-X data obtained in HH polarization, we analysed the C-band SAR polarization models and extended them to the X-band SAR data. The sea surface wind speeds were retrieved using the X-band GMF from pairs of TS-X images obtained in dual-polarization mode (i.e. VV and HH). The retrieved results were also validated by comparing with QuikSCAT measurements and the results of the German Weather Service (DWD) atmospheric model. The obtained RMS was 2.50 m s−1 when compared with the co-located wind measurements derived from the QuikSCAT, and the absolute error was 2.24 m s−1 when compared with DWD results. [ABSTRACT FROM AUTHOR]