Highly reliable and bendable dielectrics are desired in flexible or bendable electronic devices for future applications. Hexagonal boron nitride (h-BN) can be used as bendable dielectric due to its wide band gap. Here, we fabricate high quality h-BN films with controllable thickness by a low pressure chemical vapor deposition method. We demonstrate a parallel-plate capacitor using h-BN film as the dielectric. The h-BN capacitors are reliable with a high breakdown field strength of ~9.0 MV/cm. Tunneling current across the h-BN film is inversely exponential to the thickness of dielectric, which makes the capacitance drop significantly. The h-BN capacitor shows a best specific capacitance of 6.8 μF/cm², which is one order of magnitude higher than the calculated value.