A MoSe2 nanosheet/Si heterojunction photodetector with a graphene electrode was fabricated via mechanical exfoliation. This work demonstrates that graphene significantly enhances carrier mobility within the MoSe2 nanosheets, thereby facilitating efficient separation and transport of photogenerated carriers from the heterojunction interface to the top electrode. This mechanism consequently leads to a substantial improvement in overall device performance. The fabricated device demonstrates a rectification ratio of 1294.3 at room temperature. Under 650 nm red light illumination, it exhibits a responsivity (R) of 229.8 A/W, a specific detectivity (D*) of 1.9 × 1012 Jones, and an external quantum efficiency (EQE) of 4.5 × 104%. Under 405 nm blue light illumination, it achieves an R of 201.9 A/W, a D* of 1.7 × 1012 Jones, and an EQE of 6.2 × 104%. The device demonstrates broadband photodetection capability across the visible to near-infrared spectrum, featuring the fastest measured rise and fall times of 810 and 950 μs at 700 nm wavelength. Furthermore, temperature-dependent measurements reveal a significant impact on optoelectronic properties: At low temperatures, the photoresponse performance deteriorates due to the reduction of the effective barrier height within the device.