The multi-phase field model is employed to simulate the growth of tilted dendrites during directional solidification. In this simulation, the evolution of a single oriented dendritic array and the overgrowth behavior between two converging grains with different orientations are studied. The simulated results show that the dendritic tip undercooling increases with the tilt angle, which means that the tip position of tilted dendrite is always lower than that of the non-tilted in the same condition. The favorably oriented grain always blocks the unfavorably oriented one in the case of converging growth. However, when the pulling velocity is low, the growth of the preferred crystalline orientation dendrites at the grain boundary is lagged by the immediate unfavorably ones because of the solutal interaction, which may result in the fact that the unfavorably oriented grain overgrows the favorably oriented one.