Surface plasmon resonance sensors have been widely used in various fields for label-free and real-time detection of biochemical species due to their high sensitivity to the refractive index change of the surrounding environment. The common practices to achieve the improvement of sensitivity are to adjust the size and morphology of the sensor structure. This strategy is tedious and, to some extent, limits the applications of surface plasmon resonance sensors. Instead, the effect of the incident angle of excited light on the sensitivity of a hexagonal Au nanohole array sensor with a period of 630 nm and a hole diameter of 320 nm is theoretically investigated in this work. By exploring the peak shift of reflectance spectra of the sensor when facing a refractive index change in (1) the bulk environment and (2) the surface environment adjacent to the sensor, we can obtain the bulk sensitivity and surface sensitivity. The results show that the bulk sensitivity and surface sensitivity of the Au nanohole array sensor can be improved by 80% and 150%, respectively, by simply increasing the incident angle from 0° to 40°. The two sensitivities both remain nearly unchanged when the incident angle further changes from 40° to 50°. This work provides new understanding of the performance improvement and advanced sensing applications of surface plasmon resonance sensors.