A novel radiation cancelling filtering rectangular dielectric resonator antenna (DRA) with artificial magnetic conductor (AMC) surface is investigated. Based on the image theory, the combination of magnetic current and AMC can realize radiation cancelling in the whole space. To verify the presented filtering method, the rectangular AMC element with the in-phase reflection point at 6 GHz is designed. Further, the rectangular DRA with AMC surface operating in the 5.8 GHz is designed and simulated. The TEy 1d1 mode of the rectangular DRA is excited by probe. The DRA achieves radiation cancellation at about 6GHz. In addition, the dual-band AMC is designed and the related notch filter with dual radiation nulls is constructed. The nulling depths of the gain curve are greater than 23 dB.