  Based on SDSS DR8, we have selected a sample of 1728 red horizontal branch
stars with |Z|<3 kpc by using a color-metallicity relation and stellar
parameters. The sample stars clearly trace a typical thick disk population with
peaks at |Z|=1.26 kpc and [Fe/H]=-0.54. The vertical metallicity gradient of
the thick disk is estimated in two ways. One is a fit to the Gaussian peaks of
the metallicity histograms of the thick disk by subtracting minor contributions
from the thin disk and the inner halo based on the Besancon Galaxy model. The
resulting gradient is -0.12+-0.01 dex/kpc for 0.5 <|Z| <3 kpc. The other method
is to linearly fit the data based on stars with 1 <|Z| <3 kpc being the main
component of the thick disk. Five subgroups are then selected in different
directions in the X-|Z| plane to investigate the difference in the vertical
metallicity gradient between the Galactocenter and anti-Galactocenter
directions. We found that a vertical gradient o-0.22+-0.07 dex/kpc is detected
for five directions except for one involving the pollution of stars from the
bulge. The results indicate that the vertical gradient is dominant, but a
radial gradient has a minor contribution for the thick disk population
represented by RHB stars with 1 <|Z| <3 kpc. The present work strongly suggests
the existence of a metallicity gradient in the thick disk, which is thought to
be negligible in most previous works in the literature.
