A photodetector based on Graphene/n-type Si Schottky junction is designed and fabricated. I-V and C-V characteristics are analyzed from the band energy perspective. The results show that Graphene/SiN_x/Si(metal/insulation layer/semiconductor) capacitor has effects on device characteristics. Under the illumination of near-infrared light(808 nm), the photodetector exhibits that the reverse photocurrent is approximately the same value as the forward one owing to photo-generated holes, which diffuse from Si/SiN_x interface to Graphene/Si junction and the responsivity is 0.26 A/W. The Schottky barrier height and ideality factor extracting from I-V dark current curve are 0.859 eV and 2.3 respectively based on thermionic emission model. The Schottky barrier height extracting from C^-2-V curves on account of the equation of depletion layer capacitance increases and tends to be stable around 0.82 eV with increasing frequency. The value of depletion layer width of Gr/Si Schottky junction increases with increasing frequency, while doping concentration of Si donor atoms and capacitance of device decrease, which are attributed to surface states.