Numerical simulation based on the phase field method is developed to describe the solidification process of pure material in a forced convection. The effects of forced convection, undercooling, coupling parameter and anisotropy on the dendritic growth are investigated. These results indicate that the crystal grow exhibits an asymmetrical dendritic in a forced convection. The upstream arm tip growth is promoted and inhibited on the downstream arm, while restrained for the perpendicular arm. With the increase of undercooling, coupling parameter and anisotropy, the dendritic arm growth velocities increase in the three different directions