Abstract: A polyolefin is producing by polymerizing ethylene or copolymerizing ethylene and the other .alpha.-olefin at 50.degree. to 100.degree. C. in a hydrocarbon solvent in the presence of a catalyst system of an organoaluminum compound and a transition metal compound component which is a solid catalytic component containing a magnesium compound and a titanium compound under the condition (a) two step polymerizations of a first polymerization step and a second polymerization step in the presence of a reaction mixture obtained by said first polymerization step; (b) a polymerization in the presence of hydrogen at a molar ratio of H.sub.2 to C.sub.2 H.sub.4 (vapor phase) of 0.01-0.8 to produce a polymer A having a viscosity average molecular weight of 2.times.10.sup.5 -7.times.10.sup.5 at a ratio of 30 to 70 wt. % based on the total polymer in one of said first or second polymerization step and a polymerization in the presence of hydrogen at a molar ratio of H.sub.2 to C.sub.2 H.sub.4 (vapor phase) of 1.