Diamond is a wide bandgap semiconductor that can work at high temperatures and resist very high electric fields. It endures harsh environments through its physical stability and conducts heat very well. These properties make diamond suitable for the fabrication of unique electronic devices. In particular, diamond field effect transistors (FETs) have promising applications, including high-power converters for trains and electric vehicles and high-power high-frequency amplifiers for telecommunications and radar. Although high mobility is desirable for these applications, it has been difficult to achieve in diamond FETs particularly when the carrier density is high. The low mobility is most probably due to fixed and trapped charges in the non-ideal amorphous gate dielectric and at the dielectric/diamond interface. Here, we report on diamond FETs with monocrystalline hexagonal boron nitride (h-BN) as a gate dielectric. Thanks to the low density of charged impurities in monocrystalline h-BN, we obtained unprecedentedly high mobilities (>300 cm2 V−1 s−1) for moderately high carrier densities (>5 × 1012 cm−2). The resulting minimum sheet resistance was exceptionally low (<3 kΩ). Our results show that a heterostructure consisting of monocrystalline h-BN and diamond is an excellent platform with which to manufacture high-performance electronic devices.