A dual-band artificial magnetic conductor (AMC) composed of dual-layer mushroom type unit cells is researched. The dual-band AMC is composed of two capacitive metallic patch layers and via-holes connecting them to the ground plane. The equivalent circuit model of the dual-band AMC is proposed and the reflection phases calculated using the model is compared with full-wave simulation results for its validation. To overcome the limitations of the conventional reflection phase control methods such as changing the gap between the patches and varying the thickness of the substrates, the methods of adding multiple via-holes to either the lower or the upper substrates, or to both of them are proposed. The various results with different distance between the added multiple via-holes and the via-hole at the center of the patch are presented and show that the proposed methods can be used to control the reflection phase of the dual-band AMC more freely, which is expected to be useful for both dual-band AMC and electromagnetic gradient surface (EGS) designs.