High-quality ZnCr2O4 (ZCO) thin films were epitaxially grown on economical c-sapphire substrates by pulsed laser deposition (PLD) for the first time, using a ZCO ceramic target and various deposition oxygen pressures. X-ray diffraction results revealed that the as-grown ZCO films consisted of a single spinel phase, and exhibited out-of-plane and in-plane orientations with respect to the c-sapphire substrate of ZCO (1 1 1)parallel to Al2O3 (0 0 0 1) and ZCO [0 1 -1]parallel to Al2O3 [1 -1 0], respectively. Due to domain matching with a tiny misfit of 0.015%, high-quality epitaxy of (1 1 1)-ZCO on c-sapphire was achieved with typical (2 2 2) rocking-curve half width of similar to 0.07 degrees and phi-scan half width of similar to 1.85 degrees. Moreover, the films exhibited very smooth surface with a minimum root-mean-square roughness of 0.585 nm. As the deposition oxygen pressure was increased, the atomic ratio of Zn/Cr in the ZCO films was found to increase linearly from 0.316 to 0.585, while the bandgap of the ZCO films increased simultaneously from 3.61 eV to 3.87 eV. The widening of bandgap was attributed to the enhancement of cations-anions interaction and reduction of oxygen vacancies with increasing deposition oxygen pressure. Our work provides a feasible and economical solution for the epitaxial growth of high-quality ZCO films, based on which fundamental properties and technological applications of ZCO can be further explored.