Nanometer-thick hexagonal boron nitride thin films were grown by thermal chemical vapor deposition on polycrystalline Ni, Co, and Cu substrates. A thicker and more regularly stacked film was grown on a Ni substrate, whereas a smaller film thickness and more turbostratic stacking or smaller domain size were observed on Cu. Intermediate situations were observed on Co. The substrate material dependence strongly suggests that the substrate plays an important role in h-BN growth, like it does in graphene growth, although nitrogen is almost insoluble even in Ni. Grain boundaries may accommodate boron and nitrogen atoms at a growth temperature.