© 2020 Elsevier Ltd Herein, three types of converging grain growth were investigated during directional solidification, through two-dimensional phase-field simulations. The three types were distinguished by the orientation of the favorably oriented (FO) dendrites. The growth orientation of the FO dendrites was parallel to the thermal gradient direction in type I, whereas the orientation of FO dendrites was inclined in the same and opposite lateral directions as those of the unfavorably oriented (UO) dendrites in types II and III, respectively. The largest difference between FO and UO grain inclination angles—that is, the threshold angle, for unusual overgrowth in different alloy systems were clearly different, in type I and III cases. In all three types of converging grain growth, overgrowth of UO dendrites by FO dendrites (usual overgrowth) was observed to occur more frequently than that of FO dendrites being overgrown by UO dendrites (unusual overgrowth). The asymmetry of the inclined dendrite diffusion layer caused different solute interactions in the three types of converging grain growths. Based on the different solute interactions, unusual overgrowth behavior occurred most readily in type III cases—and with most difficulty in type II cases. We also saw that the local GB orientation may alternate between FO and UO grain orientations in type III cases.