PURPOSE: To obtain a polymer having excellent mechanical properties and moldability, etc., by copolymerizing ethylene with an α-olefin at a specific temperature in the presence of a catalyst derived from a Ti compound and a reaction product of a dialkylmagnesium and an organic Al compound.

CONSTITUTION: Ethylene is made to react with a 5W6C α-olefin and a 8W18C α-olefin at ≥155°C in the presence of a catalyst derived from (A) a reaction product of a dialkylmagnesium of formula I (R1 and R2 are 1W18C alkyl or cycloalkyl) (e.g. dibutylmagnesium, butyloctylmagnesium, etc.) and an organic Al compound (e.g. ethylaluminum sesquichloride) and (B) a Ti compound of formula II (R3 is 1W10C alkyl, cycloalkyl, aryl or aralkyl; X is halogen; 0≤n≤4) (e.g. TiCl4).