Abstract Under the hypothesis of gravitational redshift induced by a central supermassive black hole, and based on line widths and shifts of redward-shifted Hβ and Fe ii broad emission lines for a sample of 1973 z < 0.8 Sloan Digital Sky Survey DR5 quasars, we measured the virial factor in determining supermassive black hole masses, usually estimated by the reverberation mapping method or the relevant secondary methods. The virial factor had been believed to be from the geometric effect of the broad-line region. The measured virial factor of Fe ii is larger than that of Hβ for 98% of these quasars. The virial factor is very different from object to object and for different emission lines. For most of these quasars, the virial factor of Hβ is larger than these averages that were usually used in determining the masses of black holes. There are three positive correlations among the measured virial factor of Hβ, dimensionless accretion rate, and Fe ii/Hβ line ratio. A positive three-dimensional correlation is found among these three quantities, and this correlation indicates that the virial factor is likely dominated by the dimensionless accretion rate and metallicity. A negative correlation is found between the redward shift of Hβ and the scaled size of the broad-line region radius in units of the gravitational radius of the black hole. This negative correlation will be expected naturally if the redward shift of Hβ is mainly from the gravity of the black hole. Radiation pressure from the accretion disk may be a significant contributor to the virial factor.