We report the physical and orbital parameters of the visible component of the spectroscopic binary HD37737 (m V = 8.03). The observations were performed with the 1.2-m telescope of the Kourovka Astronomical Observatory of the Ural Federal University in 2012 and the 6-m BTA telescope of the SAO RAS in 2007 and 2009. Radial velocities were measured separately from each spectral line of the list by the cross-correlation method with a synthetic spectrum. The latter was calculated using the grids of non-LTE model atmospheres with solar chemical compositions. A significant difference in the epochs of observations (2005–2012) allowed to refine the orbital period of the star (7 · d 84705) and the orbital elements of the binary system. We obtained an estimate of the mass function f(m) = 0.23 ± 0.02M ⊙. The best agreement between the synthetic and observed spectra is achieved at T eff = 30 000 K and log g = 3.50 according to the observations on both instruments. The obtained parameters correspond to a star of spectral type O9.5 III, with mass estimated at 26 ± 2M ⊙. The minimum mass estimate of the secondary component of the binary is 6.2 ± 0.5M ⊙. We have discovered a fact that the velocities, obtained from different spectral lines, differ, which is typical for giant stars. Engaging additional spectra, obtained in 2005 with the 2.1-m KPNO telescope, we investigated the effect of this fact on the estimate of the speed of the system’s center of mass. The difference in the velocities of various lines is approximately the same in the spectra, obtained at all the three instruments. The obtained ratios suggest that the deeper layers of the atmosphere of the star are moving with a greater velocity than the outer layers. Depending on the line, the estimate of the heliocentric velocity of the binary’s center of mass varies in the range from −11 to 1 km/s.