We analyze the radial and vertical metallicity and [alpha/Fe] gradients of the disk stars of a disk galaxy simulated in a fully cosmological setting with the chemodynamical galaxy evolution code, GCD+. We study how the radial abundance gradients vary as a function of height above the plane and find that the metallicity ([alpha/Fe]) gradient becomes more positive (negative) with increasing height, changing sign around 1.5 kpc above the plane. At the largest vertical height (2 2 kpc at the outer region, because of the lower gravitational restoring force of the disk, i.e. flaring. As a result, the fraction of younger stars with higher metallicity due to the age-metallicity relation becomes higher at the outer radii, which makes the median metallicity higher at the outer radii. Combining this result with the recently observed age-metallicity and age-velocity dispersion relation for the Milky Way thick disk stars suggested by Haywood et al. (2013), we argue that the observed (small) positive radial metallicity gradient at large heights of the Milky Way disk stars can be explained by the flaring of the younger thick and/or thin disk stars.