Alunite type compound particles represented by the following general formula (I) and having a specific value of D.sub.75/D.sub.25 when D.sub.25 is the particle diameter of particles which account for 25% of the total and D.sub.75 is the particle diameter of particles which account for 75% of the total in the cumulative particle size distribution curve measured by a laser diffraction method: M.sub.a[Al.sub.1-xM'.sub.x].sub.3(SO.sub.4.sup.2-).sub.y(OH).sub.z.mH.sub- .2O (I) wherein M is at least one cation selected from the group consisting of Na.sup.+, K.sup.+, NH.sub.4.sup.+ and H.sub.3O.sup.+, M' is at least one cation selected from the group consisting of Cu.sup.2+, Zn.sup.2+, Ni.sup.2+, Sn.sup.4+, Zr.sup.4+ and Ti.sup.4+, and a, m, x, y and z satisfy 0.8.ltoreq.a.ltoreq.1.35, 0.ltoreq.m.ltoreq.5, 0.ltoreq.x.ltoreq.0.4, 1.7.ltoreq.y.ltoreq.2.5, and 4.ltoreq.z.ltoreq.7, respectively. The above particles of the present invention have a small average particle diameter, are spherical, disk-like or hexagonal and have an extremely narrow particle size distribution.