The masses of the central supermassive black holes and the Eddington ratios for a sample of 65 young radio galaxies [ 27 gigahertz-peaked spectrum ( GPS ) and 38 compact steep-spectrum ( CSS ) sources ] are estimated by various methods . We find that the average BH mass of these young radio galaxies is < \log M _ { bh } > \simeq 8.3 , which is less than that of radio loud QSOs and low redshift radio galaxies ( < \log M _ { bh } > \simeq 9.0 ) . The CSS/GPS sources have relatively high Eddington ratios with average ratio < \log L _ { bol } / L _ { Edd } > = -0.56 , which are similar to those of narrow line Seyfert 1 galaxies ( NLS1s ) . It suggests that the CSS/GPS sources may not only be in the early stage of radio activities , but also in the early stage of their accretion activities . We find that the young radio galaxies as a class deviate systematically from the M _ { bh } - \sigma _ { * } relation defined by nearby inactive galaxies , when using \sigma _ { [ O III ] } as a surrogate for the stellar velocity dispersion \sigma _ { * } . There is no significant correlation between the deviation of the [ O III ] emission line width , \Delta \sigma \equiv \sigma _ { [ O III ] } - \sigma _ { [ pred ] } , and the jet/accretion power , where \sigma _ { [ pred ] } are calculated from the Tremaine et al . relation using the estimated BH masses . However , we find that the deviation \Delta \sigma in young radio galaxies is well correlated with the Eddington ratio , and this correlation is found to be similar to that of radio quiet AGN ( QSOs/NLS1s ) where the radio jet is absent or weak . We suggest that the accretion activities may still play an important role in shaping the kinematics of [ O III ] narrow line in these young radio galaxies .