  We study the possibly existing anisotropy in the accelerating expansion
universe with the Union2 Type Ia supernovae data and Gamma-ray burst data. We
construct a direction-dependent dark energy model and constrain the anisotropy
direction and strength of modulation. We find that the maximum anisotropic
deviation direction is $(l,\,b)=(126^{\circ},\,13^{\circ})$ (or equivalently
$(l,\,b)=(306^{\circ},\,-13^{\circ})$), and the current anisotropy level is
$g_0=0.030_{+0.010}^{-0.030}$ ($1\sigma$ confidence level with Union2 data).
Our results do not show strong evidence for the anisotropic dark energy model.
We also discuss potential methods that may distinguish the peculiar velocity
field from the anisotropic dark energy model.
