  We present an evaluation of the running coupling constant for Nf=2+1 QCD. The
Schroedinger functional scheme is used as the intermediate scheme to carry out
non-perturbative running from the low energy region, where physical scale is
introduced, to deep in the high energy perturbative region, where conversion to
the MS-bar scheme is safely performed. Possible systematic errors due to the
use of perturbation theory occur only in the conversion from three-flavor to
four-flavor running coupling constant near the charm mass threshold, where
higher order terms beyond 5th order in the $\beta$ function may not be
negligible.
  For numerical simulations we adopted Iwasaki gauge action and
non-perturbatively improved Wilson fermion action with the clover term. Seven
renormalization scales are used to cover from low to high energy region and
three lattice spacings to take the continuum limit at each scale.
  A physical scale is introduced from the previous Nf=2+1 simulation of the
CP-PACS/JL-QCD collaboration, which covered the up-down quark mass range
heavier than $m_\pi\sim 500$ MeV.
