The infrared (IR) absorption and resonant Raman spectra of the undoped AA-stacking bilayer graphene have been calculated using density-functional theory in the local density approximation. It is found that the undoped AA-stacking bilayer graphene exhibits a different characteristic jump and peak structure in its IR spectra, and a different G-band peak structure in its resonant Raman spectra, compared with those of the AB-stacking one, which are caused by the different interlayer coupling effects, due to different stacking types in both of them. Based upon the different IR and Raman spectra, a powerful experimental method can be proposed to identify accurately the stacking type and the layer number in future experiments.