NOVELTY - Provided is an apparatus for drying sludge by using heat of combustion of waste plastics as heat source instead of using oils, thereby reducing cost of sludge dry.    DETAILED DESCRIPTION - The apparatus comprises a carbonized gas furnace(120) with a carbonized gas collector(123), a supply pipe(124) for exhausting the collected carbonized gas, a first nozzle(122) and a first high pressure blower(121); a combustion furnace(130) with a regeneration fuel burner(136) for burning a mixture gas of the carbonized gas generated from the carbonized gas furnace(120) and a second combustion air, and a supply pipe(137) for exhausting hot air heated by the burner(136); an air mixer(140) having a connection duct(142), a third nozzle(141) and a hot air exhausting pipe(144) for mixing and heating a gas delivered through a third high pressure blower(143), a connection duct(142) and a third nozzle(141) and generating hot air through the hot air exhausting pipe(144); and a rotary kiln(150) having a rotating cylinder(151) connected to the hot air exhausting pipe(144), a sludge input unit(152) for introducing sludge to the rotating cylinder(151), a motor(153) for rotating the rotating cylinder(151), a gear assembly(154), a rotary kiln hood(155), a cooler and an exhausting unit(156), wherein the rotary kiln(150) receives sludge by a sludge input unit(152) and hot air from the air mixer(140) to the rotating cylinder(151) and rotates slowly the rotating cylinder(151) to dry the sludge. The method comprises the steps of introducing waste synthetic resins to the carbonized gas furnace; burning the synthetic resins using a first combustion air and generating carbonized gas; introducing the carbonized gas and a second combustion gas to the combustion furnace and generating hot air of 900deg. C; introducing the hot air into the air mixer, mixing the hot air and room temperature air and generating a heated air with a predetermined temperature; introducing the heated air and set sludge into the rotary kiln; mixing the heated air and the wet sludge to dry the sludge; and exhausting vapor and heated air from the rotary kiln.