Through accelerated corrosion tests, the damage processes of the concretes containing different mineral admixtures(high calcium fly ash(HFA), ground granulated blast furnace slag(GGBFS) and silica fume(SF)) in simulated acid rain solutions(pH=2) were investigated by sphere indentation and ultrasonoscope methods. The results show that the addition of suitable mineral admixtures can retard the damage process of concretes caused by acid rain and improve its resistance to some extent, especially for those with HFA, GGBFS and SF added together. The improvement results from the pozzolanic effect of mineral admixtures to reduce the content of Ca(OH)2 in concretes and make their microstructure more density. However, the function is finite as a whole and the concretes containing mineral admixtures can still suffer severe damage under the sustaining action of acid rain attack. The deterioration of the concretes containing mineral admixtures in acid rain solutions is caused by the dissolving erosion of H+ and the expanding erosion of SO4 2- together.