We apply an iterative inversion scheme, initially developed by Hashida and Shimazaki (1984) and later modified by Joshi et al., (2010), to estimate three - dimensional shear - wave quality factor, Qs(f), of south-central Gulf of California, Mexico. An area of 230 km x 288 km in this region is divided into 108 rectangular blocks of different Qs(f). We use 25 well-located earthquakes recorded at three broadband stations of the regional network RESBAN operated by CICESE (Centro de Investigación Científica y de Educación Superior de Ensenada, Baja California) and three Ocean Bottom Seismographs (OBS) of the Sea of Cortez Ocean Bottom Array (SCOOBA) experiment. This dataset permits us to obtain Qs(f) estimates of different blocks using the modified inversion algorithm. Qs(f) is obtained at various frequencies in 0.16 - 7.94 Hz range. We found that the estimated Qs structure correlates with geological and tectonic models of the region proposed in previous studies. A regional frequency-dependent relation using all 1944 values of shear-wave quality factor is obtained at 18 different frequencies in all blocks can be approximated by a function of the form Qs(f) = 20 f 1.2. This relation is typical in a tectonically active region with high S-wave attenuation and is similar to attenuation relations reported by other authors for the Imperial Valley, California region.