A propylene block copolymer having a specified composition and consisting of a xylene soluble portion at 20.degree. C. in an amount of 5 wt % or more and a portion excluding the CXS portion, the melting temperature of the CXIS portion measured by a differential scanning caloriemeter being 130 to 155.degree. C., wherein the difference in transparency in terms of haze between prior to and posterior to the 1-hour treatment at 110.degree. C of a 150 .mu.m thick film obtained by forming said copolymer into a film by extrusion is 8% or less.According to the present invention, a block copolymer having a good transparency and improved impact resistance at a low temperature, and further exhibiting less bleeding at high-temperature heat treatment, can be provided.