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 .