There is observational evidence that broad-line regions (BLRs) exist in most active galactic nuclei (AGNs), but their origin is still unclear. One scenario is that the BLRs originate from winds accelerated from the hot coronae of the disks, and the winds are suppressed when the black hole is accreting at low rates. This model predicts a relation between (m) ((m) = (M)/(M)Edd) and the FWHM of broad emission lines. We estimate the central black hole masses for a sample of bright AGNs by using their broad Hβ line-widths and optical luminosities. The dimensionless accretion rates (m) = (M)/(M)Edd are derived from the optical continuum luminosities by using two different models: using an empirical relation between the bolometric luminosity Lbol and the optical luminosity ((m) = Lbol/LEdd, a fixed radiative efficiency is adopted); and calculating the optical spectra of accretion disks as a function of (m). We find a significant correlation between the derived (m) and the observed line width of Hβ,FWHM∝ (m)-0.37, which almost overlaps the disk-corona model calculations, if the viscosity α≈ 0.1 - 0.2 is adopted. Our results provide strong evidence for the physical link between the BLRs and accretion disks in AGNs.