Hexagonal boron nitride (h-BN) with a certain thickness has wide applications in semiconductor electronic devices. In this study, the relationship between the amount of ammonia borane and the thickness of h-BN films was investigated via low-pressure chemical vapor deposition (LPCVD) on a noncatalytic c-plane Al2O3 substrate. Through various characterization methods, the grown film was confirmed to be h-BN. The effect of the precursor mass on the growth thickness of the h-BN film was studied, and it was found that the precursor mass significantly affected the growth rate of the h-BN film. The results from SEM show that the amount of ammonia borane is 2000 mg and a 1.295-μm h-BN film is obtained. It will provide an experimental reference for the growth of thicker h-BN materials to prepare high-efficiency neutron detectors for radiation detection.