A propylene block copolymer produced by polymerizing propylene, ethylene and an .alpha.-olefin having 4 to 8 carbon atoms in two stages with a Zieglar-Natta catalyst by a process which comprises (A) supplying propylene and ethylene in the first stage and propylene and the .alpha.-olefin in the second stage, or (B) supplying propylene and the .alpha.-olefin in the first stage and propylene and ethylene in the second stage, to the polymerization system, wherein the amounts of propylene and ethylene supplied in the first stage of (A) or in the second stage of (B) are 90 to 99 wt % and 10 to 1 wt % based on the total amount of propylene and ethylene supplied in the first stage of (A) or in the second stage of (B), respectively, the amounts of propylene and the .alpha.-olefin supplied in the second stage of (A) or in the first stage of (B) are 60 to 98 wt % and 40 to 2 wt % based on the total amount of propylene and the .alpha.-olefin supplied in the second stage of (A) or in the first stage of (B), respectively, and the amounts of copolymers formed in the first and second stages are 20 to 90 wt % and 80 to 10 wt % based on the final block copolymer, respectively.