The novel transition metal compound of the invention is represented by the following formula (I): ##STR1## wherein M is a transition metal; R.sup.1 is a hydrocarbon group of 2 to 6 carbon atoms, R.sup.2 is an aryl group of 6 to 16 carbon atoms; X.sup.1 and X.sup.2 are each a halogen atom or the like; and Y is a divalent hydrocarbon group, a divalent silicon-containing group or the like. An olefin polymerization catalyst component of the present invention comprises the aforementioned transition metal compound. An olefin polymerization catalyst of the present invention comprises the aforementioned olefin polymerization catalyst component. The propylene homopolymer, the propylene copolymer and the propylene elastomer according to the present invention have such properties that the triad tacticity of propylene units chain is high, a proportion of the inversely units based on the 2,1-insertion of propylene monomer is in the specific range, and the intrinsic viscosity [.eta.], as measured in decahydronaphthalene at 135.degree. C., is in the specific range.