The invention discloses a device for removing acid gases in garbage incineration smoke at the high temperature. The device comprises a material separation hopper, a primary feed hopper, a secondary feed hopper, a tertiary feed hopper, a primary cross flow moving bed reactor, a secondary cross flow moving bed reactor, a tertiary cross flow moving bed reactor, a primary adjustable star discharge device, a secondary adjustable star discharge device, a tertiary adjustable star discharge device, a smoke inlet, a smoke outlet, a recovery bin, a drier, an implementing bin, a fresh material implementing bin, a garbage incineration smoke pipeline and an air preheater. The invention further discloses a method for removing the acid gases in the garbage incineration smoke at the high temperature. According to the invention, multiple stages of cross flow moving bed reactors are adopted, the garbage incineration smokes at moderate and high temperatures sequentially pass through the cross flow moving bed reactors and are in contact with adsorbents in the reactors to perform multi-stage deep acid gas removal, reduce corrosion and blockage by the acid gases on pipelines and equipment, and achieve the exhaust of the garbage incineration smoke in a purifying way.