There is provided a refuse-trapping cover for a portable working machine, which is capable of reducing the deterioration of the engine-cooling performance of the cooling fan that may be caused by the fibrous sawdust of a palm tree. The refuse-trapping cover includes a frame (40) having a plurality of open windows (40a-40j) and attached to the outer casing (20) of a chain saw (1) to thereby cover the air inlet slits (22), and a mesh member (50) integrally fixed to the frame (40) to thereby cover open windows (40a-40j). The frame (40) is constructed to have predetermined dimension and configuration, and the mesh member (50) is fixed to a predetermined location of the frame (40) to thereby provide a sufficient space (S) between the mesh member (50) and the outer casing (20) to avoid the mesh member (50) from being adsorbed onto the outer casing (20).