A propylene-ethylene random copolymer prepared by copolymerizing propylene with ethylene in the substantial absence of a liquid medium with a catalyst system comprising:(A) a solid catalyst component containing magnesium, titanium, a halogen and a first electron donor as an essential component,(B) an organoaluminum compound and(C) a second electron donor compound, wherein an ethylene content (E) of the copolymer is from 3.5 to 7.0% by weight, and wherein a content of a xylene-soluble portion at 20.degree. C. (D) of the copolymer satisfies the relationship D.ltoreq.E+2.0 (% by weight). Films of the copolymer have an excellent appearance (little bleed whitening) and an excellent balance between low-temperature heat-sealing property and rigidity.