  We report on the bright Lyman-break galaxies (LBGs) selected in a 767
arcmin^2 area of the Subaru Deep Field. The selection is made in the i-zR vs
zB-zR plane, where zB and zR are new bandpasses with a central wavelength of
8842A and 9841A, respectively. This set of bandpasses enables us to separate
well z~6 LBGs from foreground galaxies and Galactic cool stars. We detect 12
LBG candidates down to zR=25.4, and calculate the normalization of the
rest-frame far-ultraviolet (FUV: 1400A) luminosity function at MFUV = -21.6 to
be \phi(-21.6) = (2.6+/-0.7) x 10^{-5} mag^{-1} Mpc^{-3}. This must be the most
reliable measurement ever obtained of the number density of bright z~6 LBGs,
because it is more robust against both contamination and cosmic variance than
previous values. The FUV luminosity density contributed from LBGs brighter than
MFUV = -21.3 is (2.8+/-0.8) x 10^{24} ergs/s/Hz/Mpc^3, which is equivalent to a
star formation rate density of (3.5+/-1.0) x 10^{-4} Msun/yr/Mpc^3. Combining
our measurement with those at z<6 in the literature, we find that the FUV
luminosity density of bright galaxies increases by an order of magnitude from
z~6 to z~3 and then drops by 10^3 from z~3 to the present epoch, while the
evolution of the total luminosity density is much milder. The evolutionary
behavior of bright LBGs resembles that of luminous dusty star-forming galaxies
and bright QSOs. The redshift of z~3 appears to be a remarkable era in the
cosmic history when massive galaxies were being intensively formed.
