An alumina porous body which comprises coarse alumina particles as a filler and SiO.sub.2, said alumina and SiO.sub.2 forming an Al.sub.2 O.sub.3 -SiO.sub.2 compound (mullite) on the surface of the coarse alumina particles through the reaction between them that takes place at the time of firing, said compound binding said coarse alumina particles, forming pores between them. The invention also relates to a process for producing an alumina porous body which comprises mixing coarse alumina particles with SiO.sub.2, molding the mixture, and firing the molding at a temperature not higher than 1700.degree. C., thereby sintering the coarse alumina particles.