An incinerator with a moving-bed stoker in which a chain conveyor is inclined in the direction of its movement and a plurality of fuel- or fire-bed members L-shaped in cross section are mounted on the links of the chain conveyor, whereby a step-like moving fuel- or fire-bed is defined. Each fuel- or fire-bed member comprises an upright or vertical plate and a horizontal plate and combustion air injection holes are formed through the upright or vertical plate so that the foreign matter such as ash, metal pieces or the like as well as the molten ash produced as the result of the combustion of waste with a low melting point can be prevented from falling through the combustion air holes into the stoker.