We present a perfect graphene absorber with a compound waveguide grating at the near-infrared. The analytical approach is mainly based on the coupled leaky mode theory, which turns the design of the absorber to finding out the required leaky modes supported by the grating structure. Perfect absorption occurs only when the radiative loss of the leaky mode matches the intrinsic absorption loss, which is also named the critical coupling condition. Furthermore, we also demonstrate that the critical coupling of the system can be robustly controlled, and the perfect absorption wavelength can be easily tuned by adjusting the parameters of the compound waveguide grating.