The phase-field model coupled with a flow field was used to simulate the dendrite growth in the undercooled pure metal melt. The effects of flow velocity, supercooling and anisotropy on the dendritic growth were studied. Results indicate that melt flow can enhance the emergence of side-branches, the morphology of the dendrite was composed of the principal branches and side-branches. With an increase in flow velocity and supercooling, the velocity of upstream dendritic tip increases, but the tip radius decreases first and then increases. With an increase in anisotropy values, the velocity of upstream dendritic tip increases and the tip radius decreases. The results of calculation agreed with LMK theory in the case of low flow velocity and anisotropy.