A two-stage garbage incinerator is characterized in that secondary air supply holes are arranged on front and rear arches of a furnace body and an ignition combustion-supporting hole is arranged on the rear arch; a grate in the furnace body is divided into two stages from top to bottom; the upper stage is a forward pushing stage and the lower stage is a backward pushing stage; an independent primary air chamber is arranged below each stage; the heads of the grates on the forward pushing stage face the low point direction of the grates; the heads of the grates on the backward pushing stage face the high point direction of the grates; moving beams of the grates on the same stage are equipped with left and right draw bars arranged side by side; the left and right draw bars are supported by supporting roller devices and are connected with the moving beams to form draw bar frames; and the ends of the draw bar frames are connected with front rocker arm driving mechanisms, lateral rocker armdriving mechanisms or front straight driving mechanisms. The incinerator can realize full drying of the whole garbage material, ensure complete combustion and ensure the garbage incineration effect and hot ignition loss rate. At the same time, the incinerator has less spare parts and spare part specifications, good quick-wear part interchangeability and low manufacture and maintenance costs.