To provide a drying process of waste such as sludge, by which an odor component in waste steam generated when such waste is dried, can be removed and the resulting waste steam free from such an odor component can be discharged to the outside, and also to provide a drying device for the drying process.

This drying device is provided with a drying vessel 5; a high- temperature oxidative deodorization furnace 3; a pipeline 15 for connecting the drying vessel 5 to the high-temperature oxidative deodorization furnace 3 so that waste steam generated by drying a material to be dried in the drying vessel 5, is introduced into the high-temperature oxidative deodorization furnace 3; a jacket 6 placed outside the drying vessel 5; and a pipeline 16 for connecting the high-temperature oxidative deodorization furnace 3 to the jacket 6 so that a high-temperature and high-humidity gas formed in the deodorization furnace 3 is introduced into the jacket 6 to heat a heat transfer surface 4 (inner wall surface of the drying vessel 5); wherein an odor component contained in the above waste steam is decomposed in the high-temperature oxidative deodorization furnace 3, and concurrently, the high-temperature and high- humidity gas is formed in the deodorization furnace 3 and introduced into the jacket 6 to heat the heat transfer surface 4 and thereafter, discharged to the outside of the device.