Large-area single-crystal monolayers of two-dimensional (2D) materials such as graphene1,2,3, hexagonal boron nitride (hBN)4,5,6 and transition metal dichalcogenides7,8 have been grown. hBN is considered to be the ‘ideal’ dielectric for 2D-materials-based field-effect transistors (FETs), offering the potential for extending Moore’s law9,10. Although hBN thicker than a monolayer is more desirable as substrate for 2D semiconductors11,12, highly uniform and single-crystal multilayer hBN growth has yet to be demonstrated. Here we report the epitaxial growth of wafer-scale single-crystal trilayer hBN by a chemical vapour deposition (CVD) method. Uniformly aligned hBN islands are found to grow on single-crystal Ni (111) at early stage and finally to coalesce into a single-crystal film. Cross-sectional transmission electron microscopy (TEM) results show that a Ni23B6 interlayer is formed (during cooling) between the single-crystal hBN film and Ni substrate by boron dissolution in Ni. There are epitaxial relationships between hBN and Ni23B6 and between Ni23B6 and Ni. We also find that the hBN film acts as a protective layer that remains intact during catalytic evolution of hydrogen, suggesting continuous single-crystal hBN. This hBN transferred onto the SiO2 (300 nm)/Si wafer acts as a dielectric layer to reduce electron doping from the SiO2 substrate in MoS2 FETs. Our results demonstrate high-quality single-crystal multilayered hBN over large areas, which should open up new pathways for making it a ubiquitous substrate for 2D semiconductors.