Directional solidification (DS) has been widely used to produce aero-engine and gas turbine blades of nickel-based superalloys. The preferred crystallographic orientation of nickel-based superalloys is [001], so the [001] columnar-grain structure can form after DS. Due to the low Young's modulus and the elimination of transverse grain boundaries, the [001] columnar-grain structure has beneficial mechanical behavior. The competitive grain growth dominates the production of columnar grains. There are two views about competitive grain growth, which are consistent for diverging grains but not consistent for converging grains. In the case of convergence of the first view, the grain boundary (GB) was parallel to the favorably aligned dendrites, which indicates that the favorably aligned grain cannot be eliminated. For converging grains of the second view, not only the favorably aligned dendrites could block unfavorably aligned ones, but also the unfavorably aligned dendrites could block favorably aligned ones. Thus, the converging grain boundary moved from unfavorably aligned grain to favorably aligned grain. Finally, the favorably aligned grain may be eliminated. The study about the two views was carried out in the case of the same secondary orientation but did not taken into account the secondary orientation. Up to now, the literatures about the effect of secondary dendrite orientation on competitive growth is rarely and their views contradict with each other. In this work, the bi-crystal and ter-crystal plates with different secondary orientations were produced to study the influence of secondary orientation on competitive grain growth. For the bi-crystal with the same primary orientation, as the secondary GB angle increased, the GB was nearly at the middle of the plate sample, which indicated that the competitive grain growth was weak and could be neglected. For the ter-crystal with different primary orientations, not the secondary orientation but the primary orientation could obviously affect competitive grain growth. In the case of converging grains, the change of secondary dendrite orientation had no effect on the competitive growth behavior and grain growth rate; the favorably and unfavorably aligned dendrites could block each other, which disagreed with Walton-Chalmers model and in good agreement with the results of Zhou. In the case of diverging grains, the result agreed with Walton-Chalmers model and Zhou's result.