Abstract. The binary parameters of the microquasar GRS 1915+105 have been determined by the detection of Doppler-shifted 12 CO and 13 CO lines in its K-band spectrum (Greiner et al. 2001b). Here, we present further analysis of the same K-band VLT spectra and we derive a rotational broadening of the donor star of υ sin i = 26±3 km s −1 from the 12 CO/ 13 CO lines. Assuming that the K-type star is tidally locked to the black hole and is filling its Roche-lobe surface, then the implied mass ratio is q = M d Mx = 0.058 ± 0.033. This result, combined with (P, K, i) = (33.5 d, 140 km s −1 , 66 • ) gives a more refined mass estimate for the black hole, M x = 14.0 ± 4.4 M , than previously estimated, using an inclination of i = 66 • ± 2 • (Fender et al. 1999) as derived from the orientation of the radio jets and a more accurate distance. The mass for the early K-type giant star is M d = 0.81 ± 0.53 M , consistent with a more evolved stripped-giant donor star in GRS 1915+105 than, for example, the donor star of the prototype black-hole X-ray transient, V404 Cyg which has the longest binary period after GRS 1915+105.