A vacuum cleaner dust bag that is constructed to substantially increase the filtering action of the bag and therefore is particularly adaptable for use in vacuum cleaners utilized in hospitals, nursing homes, and other health care facilities. The filter dust bag is constituted of two concentric sections or compartments with the space of one of the compartments having a dry filter mat material that effectively traps all dust and dirt particles down to minute particles of about 0.3 microns. The tube on the filter dust bag which connects to the discharge outlet of the vacuum cleaner is constructed of an air-impervious material, while the outer and inner layers of the filter are fabricated of air-pervious material of different elasticity