  We investigate the $\mbh- \sigma_*$ relation for radio-loud quasars with
redshift $z<0.83$ in Data Release 3 of the Sloan Digital Sky Survey (SDSS). The
sample consists of 3772 quasars with better model of H$\beta$ and \oiii lines
and available radio luminosity, including 306 radio-loud quasars, 3466
radio-quiet quasars with measured radio luminosity or upper-limit of radio
luminosity (181 radio-quiet quasars with measured radio luminosity). The virial
supermassive black hole mass (\mbh) is calculated from the broad \hb line, the
host stellar velocity dispersion ($\sigma_*$) is traced by the core \oiii
gaseous velocity dispersion, and the radio luminosity and the radio loudness
are derived from the FIRST catalog. Our results are follows: (1) For
radio-quiet quasars, we confirm that there is no obvious deviation from the
$\mbh- \sigma_*$ relation defined in inactive galaxies when \mbh uncertainties
and luminosity bias are concerned. (2) We find that radio-loud quasars deviate
much from the $\mbh- \sigma_*$ relation respect to that for radio-quiet
quasars. This deviation is only partly due to the possible cosmology evolution
of the $\mbh- \sigma_*$ relation and the luminosity bias. (3) The radio
luminosity is proportional to
$\mbh^{1.28^{+0.23}_{-0.16}}(\lb/\ledd)^{1.29^{+0.31}_{-0.24}}$ for radio-quiet
quasars and $\mbh^{3.10^{+0.60}_{-0.70}}(\lb/\ledd)^{4.18^{+1.40}_{-1.10}}$ for
radio-loud quasars. The weaker correlation of the radio luminosity dependence
upon the mass and the Eddington ratio for radio-loud quasars shows that other
physical effects would account for their radio luminosities, such as the black
hole spin.
