A noise suppressor for use with the vacuum air cleaner includes an enclosed casing. On the casing, there are an air intake end and an air outlet end. Between the air intake end and the air outlet end, there is the noise suppressing chamber. At the air intake end and the air outlet end, there are the air intake area and the air outlet area made up of densely arranged dust-shaped air exhaust microholes. The air intake sectional area and air outlet sectional area, which are defined by the cross-sectional area of the microholes respectively, are smaller than the sectional area of the noise suppressing chamber. A number of noise suppressing structures or arrangements may be used to form the noise suppressor. After being installed at the air exhaust port of the vacuum air cleaner, the noise suppressor can greatly reduce the noise the vacuum air cleaner gives out when in use.