The dilute granular flow distribution near the rough boundary of a two_dimensional inclined channel have been reported. It is caused by the increasing inclination and the width of the channel. Compared with the viscous fluids, the velocity profiles of the granular flow are more blunted than the parabolic form and the density profiles are nonuniform. In thie paper, we present the density of granular flux ξ near the rough boundary of a two_dimensional inclined channel. the results show that there is a critical width of channel Wc for the transition of the density of granular flux ξ=ρv, and the density of granular flux near the boundary decaying exponentially with incresaing inclination of the channel when the width of channel is less than Wc.