The ultra-wide bandgap (~6.2 eV), thermal stability and radiation tolerance of AlN make it an ideal choice for preparation of high-performance far-ultraviolet photodetectors (FUV PDs). However, the challenge of epitaxial crack-free AlN single-crystalline films (SCFs) on GaN templates with low defect density has limited its practical applications in vertical devices. Here, a novel preparation strategy of high-quality AlN films was proposed via the metal organic chemical vapor deposition (MOCVD) technique. Cross-sectional transmission electron microscopy (TEM) studies clearly indicate that sharp, crack-free AlN films in single-crystal configurations were achieved. We also constructed a p-graphene/i-AlN/n-GaN photovoltaic FUV PD with excellent spectral selectivity for the FUV/UV-C rejection ratio of >103, a sharp cutoff edge at 206 nm and a high responsivity of 25 mA/W. This work provides an important reference for device design of AlN materials for high-performance FUV PDs.