We present a general method to design multiband absorber by replacing the ground plane in a conventional metamaterial absorber with an artificial magnetic conductor. Due to its unique property of in-phase reflection at some specific frequency, the artificial magnetic conductor is used to introduce new absorption in the operation band. Meanwhile, out of the in-phase reflection band, the original absorbing capability of the absorber is reserved. To demonstrate it, we design a metamaterial absorber comprising three layers which are grids patterned resistive frequency selective surface, dielectric layer and the ground plane respectively. With an appropriate design, the absorber performs an absorbing peak at about 10 GHz. Then, we utilize a single band artificial magnetic conductor at 6.25 GHz and a dual-band one at 6.27 GHz and 8.17 GHz, which are both lossy and comprised of patches array varying in periodic size with a thickness of 0.6 mm, to replace the ground plane in the metamaterial absorber separately. The reflectivity of these multiband absorbers are simulated, and experiments are carried out later. Experimental results agree well with the simulations. All results verified that the method presented at the beginning is effective. The results show that additional absorptions exist at the frequencies where microwaves are nearly reflected in phase on the artificial magnetic conductor. Meanwhile the original absorbing capability of the metamaterial absorber has been preserved mostly. Based on the artificial magnetic conductor, the multiband absorber performs better with an increasing absorption bandwidth from 8.5 GHz to 10 GHz compared to the metamaterial absorber.