Catalyst for olefin polymerization

A catalyst for olefin polymerization which comprises a component (A) and a component (B), wherein:

• component (A) is a solid catalyst component obtained by contacting together the following components (i) to (iv):
• (i) a solid component comprising titanium, magnesium and halogen as essential elements, and which is obtained by contacting a magnesium halide with a titanium compound represented by the formula Ti(OR.sup.4).sub.4-n X.sub.n wherein R.sup.4 stands for a hydrocarbon residue having 1 to 10 carbon atoms, X stands for a halogen atom and n is a number of from 0 to 4;
• (ii) a silicon compound represented by the formula(I):
• R.sup.1.sub.m X.sub.n Si(OR.sup.2).sub.4-m-n (I)
• wherein R.sup.1 and R.sup.2 each represent a hydrocarbon residue, X represents a halogen, and each of m and n is an integer in the range of 0.ltoreq.m.ltoreq.3, 0.ltoreq.n.ltoreq.3, and 0.ltoreq.m+n.ltoreq.3,
• (iii) a titanium compound or a silicon compound represented by the formula (II) or (III):
• Ti(OR.sup.3).sub.4-l X.sub.l (II)
• R.sup.4.sub.4-l SiX.sub.l (III)
• wherein R.sup.3 represents a hydrocarbon residue, R.sup.4 represents hydrogen or a hydrocarbon residue, X represents a halogen, and l is an integer in the range of 0<l.ltoreq.4, and
• (iv) an organoaluminum compound;
• and
• component (B) is an organoaluminum compound.