The spatial (ΔGH) and the angular (ΘGH) Goos-Hänchen (GH) shifts for an Airy beam impinging upon a weakly absorbing medium coated with the monolayer graphene are theoretically investigated. The influence of the GH shift on the incident angle, the incident wavelength, the Fermi energy, and the decay factors of Airy beams is discussed. A significant magnification of ΔGH, which reaches its maximum of about three orders of wavelengths, is predicted. Our findings may provide a feasible tool to obtain a huge ΔGH in experiments.