The h-BN/diamond mix-dimensional heterostructure has broad application prospects in the fields of optoelectronic devices and power electronic devices. In this paper, the electronic properties and band offsets of hexagonal boron nitride (h-BN)/(H, O, F, OH)-diamond (111) heterostructures were studied by first-principles calculations under biaxial strain. The results show that different terminals could significantly affect the interface binding energy and charge transfer of h-BN/diamond heterostructure. All heterostructures exhibited semiconductor properties. The h-BN/(H, F)-diamond systems were indirect bandgap, while h-BN/(O, OH)-diamond systems were direct bandgap. In addition, the four systems all formed type-II heterostructures, among which h-BN/H-diamond had the largest band offset, indicating that the system was more conducive to the separation of electrons and holes. Under biaxial strain the bandgap values of the h-BN/H-diamond system decreased, and the band type occurred direct–indirect transition. The bandgap of h-BN/(O, F, OH)-diamond system increased linearly in whole range, and the band type only transformed under large strain. On the other hand, biaxial strain could significantly change the band offset of h-BN/diamond heterostructure and promote the application of this heterostructure in different fields. Our work provides theoretical guidance for the regulation of the electrical properties of h-BN/diamond heterostructures by biaxial strain.