A particle of titanium compounds is in the form of a fine agglomerate comprising crystals of an alkaline-earth metal titanate represented by RTiO.sub.3 wherein R is an alkaline-earth metal and crystals of an alkali metal titanate represented by M.sub.2 Ti.sub.n O.sub.2n+1 wherein M is an alkali metal and n is an integer of 2 to 6, or these two kinds of crystals and crystals of titanium dioxide (TiO.sub.2), the two or three kinds of crystals being mingled together. A powder composed of such particles is produced by preparing a mixture from RO wherein R is an alkaline-earth metal or an alkaline-earth metal compound becoming RO when heated, M.sub.2 O wherein M is an alkali metal or an alkali metal compound becoming M.sub.2 O when heated, and TiO.sub.2 or a titanium compound becoming TiO.sub.2 when heated, in a ratio so that Z.gtoreq.X+mY wherein Z is the number of moles of TiO.sub.2, X is the number of moles of RO, Y is the number of moles of M.sub.2 O, Z, X and Y are each a positive number, and m is 6 when Z>X+mY or m is 2 to 6 when X=X+mY, and heat-treating the mixture at a temperature of 700 to 1300.degree. C. The powder is mixed with at least a binder resin, followed by molding to prepare a friction material.