According to the dry method of the invention for purifying an exhaust gas, fine particles of a Ca-type absorbent such as dolomite are sprayed into the exhaust gas, and the absorbent particles absorbing acid harmful substances from the gas are collected by a dust collector (3) along with other particles in the exhaust gas. The collected particles are divided by a classifier (7) into a portion of coarse particles chiefly containing fly ash and a portion of absorbent particles not larger than a predetermined size, and the latter portion only is supplied to a hydration reactor (9). The absorbent particles in the reactor (9) are hydrated with superheated water vapor and thereby expanded, whereby an inactive shell formed on the surface of each particle by the absorption of the acid harmful substances is broken to reactivate the particles.; The reactivated absorbent particles are supplied to the exhaust gas again. The acid harmful substances are therefore removable efficiently with a smaller amount of absorbent.