We demonstrated strong optical absorption in a graphene integrated silicon slot waveguide. Due to the increase in light intensity and decrease of optical mode confinement in the silicon slot, the graphene experienced an increased interaction to the in-plane light. A waveguide absorption of 0.935 dB μm(-1) was measured at 1.55 μm wavelengths. Based on the graphene-on-silicon slot waveguide, a compact and high-responsivity photodetector was demonstrated. Benefited from the lack of efficient electron cooling in the suspended graphene and the intensity enhancement effect in the nano slot, a maximum responsivity of 0.273 A W(-1) was achieved in the telecommunication band.