Phase-field model was employed to quantitatively study the effect of convection on pattern selection and growth rate of 2D and 3D dendrite tip, as well as the effect of the different convection velocity on the dendritic growth. The calculated results show that crystal is asymmetric in the priority direction of growth under flow. The dentritic growth is promoted in the upstream region and suppressed in the downstream region. Convection can cause deviation in the dendrite growth direction and the preferred direction of the columnar crystals. It has been found that both primary dendrite stem and secondary dendrite arm deflect significantly towards upstream direction, secondary dendrite arm in upstream direction is more developed than the primary dendrite in downstream direction.