A process for producing a propylene random copolymer wherein the comonomer is ethylene or 1-butene satisfying the following conditions of 1) to 5): 1) a molecular weight distribution (Mw/Mn, PDI) of 2.4 or less, wherein the molecular weight distribution is determined by measuring a weight average molecular weight (Mw) and a number average molecular weight (Mn) of the propylene random copolymer using gel permeation chromatography, respectively and then calculating a ratio (Mw/Mn) of the weight average molecular weight to the number average molecular weight as the molecular weight distribution, as further described in the specification; 2) a comonomer content of 10% by weight or less, determined according to ASTM-D 5576 as further described in the specification; 3) a shrinkage ratio of 1.0% or less, as measured in accordance with ASTM D955 method by measuring a length of a mold cavity (12.7* 127*3.2mm) and a length of an injection-molded specimen of the propylene random copolymer, respectively and then dividing the change relative to the length of the mold cavity by the length of the mold cavity (shrinkage ratio = 100 * (length of mold cavity - length of inj ection-molded specimen) / length of mold cavity); 4) flexural modulus of 1,274.8465 MPa (13,000 kg/cm 2) or more, as measured in accordance with ASTM D790 method; and 5) tensile strength at yield of 290 kg/cm 2 or more, as measured in accordance with ASTM D638 method; wherein the copolymer is prepared by copolymerizing a propylene monomer and ethylene or 1-butene in the presence of a catalyst composition including a metallocene compound of the following Chemical Formula 1: in Chemical Formula 1, M is a Group 4 transition metal, X 1 and X 2 are each independently the same or different halogen, A is silicon or germanium, R 1 to R 2 are, each independently the same as or different from each other, a C 1-20 alkyl group or a C 6-20 aryl group, and R 3 to R 4 are, each independently the same as or different from each other, a C 6-20 aryl group substituted with a C 2-20 alkoxyalkyl group. 1) a molecular weight distribution (Mw/Mn, PDI) of 2.4 or less, wherein the molecular weight distribution is determined by measuring a weight average molecular weight (Mw) and a number average molecular weight (Mn) of the propylene random copolymer using gel permeation chromatography, respectively and then calculating a ratio (Mw/Mn) of the weight average molecular weight to the number average molecular weight as the molecular weight distribution, as further described in the specification; 2) a comonomer content of 10% by weight or less, determined according to ASTM-D 5576 as further described in the specification; 3) a shrinkage ratio of 1.0% or less, as measured in accordance with ASTM D955 method by measuring a length of a mold cavity (12.7* 127*3.2mm) and a length of an injection-molded specimen of the propylene random copolymer, respectively and then dividing the change relative to the length of the mold cavity by the length of the mold cavity (shrinkage ratio = 100 * (length of mold cavity - length of inj ection-molded specimen) / length of mold cavity); 4) flexural modulus of 1,274.8465 MPa (13,000 kg/cm 2) or more, as measured in accordance with ASTM D790 method; and 5) tensile strength at yield of 290 kg/cm 2 or more, as measured in accordance with ASTM D638 method; wherein the copolymer is prepared by copolymerizing a propylene monomer and ethylene or 1-butene in the presence of a catalyst composition including a metallocene compound of the following Chemical Formula 1: in Chemical Formula 1, M is a Group 4 transition metal, X 1 and X 2 are each independently the same or different halogen, A is silicon or germanium, R 1 to R 2 are, each independently the same as or different from each other, a C 1-20 alkyl group or a C 6-20 aryl group, and R 3 to R 4 are, each independently the same as or different from each other, a C 6-20 aryl group substituted with a C 2-20 alkoxyalkyl group. wherein the copolymer is prepared by copolymerizing a propylene monomer and ethylene or 1-butene in the presence of a catalyst composition including a metallocene compound of the following Chemical Formula 1: in Chemical Formula 1, M is a Group 4 transition metal, X 1 and X 2 are each independently the same or different halogen, A is silicon or germanium, R 1 to R 2 are, each independently the same as or different from each other, a C 1-20 alkyl group or a C 6-20 aryl group, and R 3 to R 4 are, each independently the same as or different from each other, a C 6-20 aryl group substituted with a C 2-20 alkoxyalkyl group. M is a Group 4 transition metal, X 1 and X 2 are each independently the same or different halogen, A is silicon or germanium, R 1 to R 2 are, each independently the same as or different from each other, a C 1-20 alkyl group or a C 6-20 aryl group, and R 3 to R 4 are, each independently the same as or different from each other, a C 6-20 aryl group substituted with a C 2-20 alkoxyalkyl group.