Novel high active catalysts useful for highly stereospecific polymerization of olefin which enables to produce polymer of low content of catalyst residue, and of good grain size having a high stereoregularity can be obtained by a combination of [A] a solid catalyst component obtained by reacting and/or grinding a specified organomagnesium component (i) with a specified chlorosilane compound containing Si-H (ii) to obtain a solid (1) and reacting said solid (1) with a titanium compound containing at least one halogen atom (2) and a carboxylic acid or a derivative thereof (3) and [B] a component consisting of an organometallic compound and a carboxylic acid or a derivative thereof. The organomagnesium component is of the formulaM.sub..alpha. Mg.sub..beta. R.sub.p.sup.1 R.sub.q.sup.2 X.sub.r Y.sub.swherein .alpha. is a number of 0 or greater than 0; .beta.>0, p, q, r, and s are each a number of 0 or greater; p+q+r+s=m.alpha.+2.beta. wherein m is the valency of M; M is a metal element of the 1st to the 3rd group of the Periodic Table; R.sup.1 and R.sup.2 are the same or different hydrocarbon radicals having 1 to 20 carbon atoms; X and Y are the same or different radicals selected from the group consisting of halogen, OR.sup.3, OSiR.sup.4 R.sup.5 R.sup.6, NR.sup.7 R.sup.8 and SR.sup.9 wherein R.sup.3, R.sup.4, R.sup.5, R.sup.6, R.sup.7 and R.sup.8 are each hydrogen atom or a hydrocarbon radical having 1 to 20 carbon atoms and R.sup.9 is a hydrocarbon radical having 1 to 20 carbon atoms, and chlorosilane is of the formulaH.sub.a SiCl.sub.b R.sub.4-(a+b)wherein a and b are each a number greater than 0, having the relationships a.ltoreq.2 and a+b.ltoreq.4 wherein R is a hydrocarbon radical having 1 to 20 carbon atoms.