  (Abridged) Using an empirical relation between the broad line region size and
optical continuum luminosity, we estimated the black hole mass and accretion
rate for 135 AGNs with double-peaked broad emission lines in two samples. With
black hole masses from $3\times 10^7M_\odot$ to $5\times 10^9M_\odot$, these
AGNs have the dimensionless accretion rates (Eddington ratios) between 0.001
and 0.1, and the bolometric luminosity between $10^{43}erg/s$ and
$10^{46}erg/s$, both being significantly larger than those of several
previously known low-luminosity double-peaked AGNs. The optical-X-ray spectra
indices, $\alpha_{OX}$, of these high-luminosity double-peaked AGNs is between
1 and 1.9. Modest correlations of the $\alpha_{OX}$ value with the Eddington
ratio and bolometric luminosity indicate that double-peaked AGNs with higher
Eddington ratio or higher luminosity tend to have larger $\alpha_{OX}$ value.
Therefore we suggested that the accretion process in some high-luminosity
double-peaked AGNs is probably different from that of low-luminosity objects
where an ADAF-like accretion flow was thought to exist. This is also supported
by the presence of possible big blue bumps in the spectra of some double-peaked
AGNs with higher Eddington ratios. We noticed that the prototype double-peaked
emission line AGN, Arp 102B, may be an ``intermediate'' object between the high
and low luminosity double-peaked AGNs. In addition, we found an apparent strong
anti-correlation between the peak separation of double-peaked profile and
Eddington ratio. If it is real, it may provide us a clue to understand why
double-peaked broad emission lines were hardly found in luminous AGNs with
Eddington ratio larger than 0.1.
