The mechanism of grain structure evolution during directional solidification is a fundamental subject in material science. Within the published research there exist conflicting views on the mechanism of grain overgrowth. To study the effect of solidification rate on grain structure evolution, bi-crystals samples were produced in a nickel-base superalloy at different solidification rates. It was found that at the convergent grain boundaries those grains better aligned with respect to the heat flux more readily overgrew neighbouring grains with misaligned orientations and the effect became more pronounced as solidification rate was increased. However, at diverging grain boundaries the rate of overgrowth was invariant to the solidification rate. These experimental results were compared with models in the literature. Thus, a better insight into competitive grain growth in directional solidification processes was obtained. The mechanism of grain structure evolution during directional solidification is a fundamental subject in material science. Within the published research there exists conflicting views on the mechanism of grain overgrowth. To study the effect of solidification rate on grain structure evolution, bi-crystals samples were produced in a nickel-base superalloy at different solidification rates. It was found that at the convergent grain boundaries that grains better aligned with respect to the heat flux more readily overgrew neighbor grains with misaligned orientations and the effect became more pronounced as solidification rate was increased. However, at diverging grain boundaries the rate of overgrowth was invariant to the solidification rate. These, a better insight into competitive grain growth in directional solidification processes was obtained.