We have investigated galaxies around NGC 6251 to search for an associated group. Our main goal is to study the environment around the giant radio galaxy to better understand the reasons for its size and structure. To this end, we have made spectroscopic observations with the 2.16-m optical telescope at Xinglong Station of the National Astronomical Observatories of China (NAOC) and obtained spectra of 45 objects (including four likely stars). The redshifts give us 10 new galaxies in a group, which are in addition to seven previously known members. The 17 galaxies' positions are compared with the radio emission. The optical velocity dispersion of group members within 0.7 Mpc of NGC 6251 is not consistent with that expected from correlation curves of X-ray luminosity Lx versus velocity dispersion σr. We briefly discuss this result, suggesting that in the NGC 6251 group, the density of X-ray emitting gas is unusually low, and this is the main reason for the size of the radio source.