Synthetic aperture radar (SAR) imagery is routinely acquired at HH-polarization in high latitude areas for measuring surface wind over the ocean. However, in the contrary of VV-polarization, there is no HH-polarization geophysical model function (GMF) exists to directly retrieve wind speed from SAR images. In general, HH-polarized Normalized Radar Cross Section (NRCS) is thus converted into VV-polarization and then conventional CMOD functions are used with auxiliary wind direction information for wind speed retrieval. In this letter, we propose a new GMF for SAR ocean surface wind speed retrieval, called CMODH, which relates the C-band NRCS acquired at HH-polarization over the ocean, to the 10-m height wind speed, incident angle and relative wind direction. We first use more than 220,000 ENVISAT ASAR radar backscatter measurements collocated with ASCAT winds to derive the CMODH coefficients. Subsequently, 1459 RADARSAT-2 (RS-2) and 428 Sentinel-1A/B (Sl-1A/B) HH-polarized SAR acquisitions under different wind speeds are matched to in situ buoy observations to validate CMODH. The statistical comparisons between SAR-observed and simulated NRCS show a bias of -0.07 dB and a root mean square error of 1.62 dB for RS-2, and -0.01 dB and 2.48 dB for S1-1A/B. These results suggest that the proposed CMODH has the potential to directly retrieve ocean surface wind speeds using C-band SAR images acquired at HH-polarization, with no need for NRCS transformation by using various empirical and theoretical polarization ratio models.