A process for producing a pelletized or molded article of a polypropylene-based resin composition having a density below 1.00 g/cm 3, comprising the steps of: melt-kneading the following components and:: propylene block copolymer having an MFR of 50 to 150 g/10 minutes and composed of a propylene homopolymer portion and a copolymer portion of propylene and another α-olefin, the propylene homopolymer portion having an isotactic pentad fraction of 98 % or more, and the copolymer portion containing propylene at 45 to 85 % by weight, and having a glass transition temperature of -40 °C or lower and a weight-average molecular weight of 500,000 to 2,000,000: 30 to 95 % by weight, and ethylene- or styrene-based elastomer having an MFR of 0.1 to 20 g/10 minutes and a density of 0.850 to 0.910 g/cm 3: 5 to 50 % by weight, supplying carbon fibers as the following component:: carbon fibers having a fiber diameter larger than 2 μm, but 15 μm or less and a fiber length of 1 to 20 mm: 0.5 to 20 % by weight, through a side feeder into the components and being molten and kneaded to disperse the carbon fibers and control the breaking of the carbon fibers to an average length of 0.05 mm or more, but below 20 mm, and extruding the resulting polypropylene-based resin composition into pellets or a molded shape. melt-kneading the following components and:: propylene block copolymer having an MFR of 50 to 150 g/10 minutes and composed of a propylene homopolymer portion and a copolymer portion of propylene and another α-olefin, the propylene homopolymer portion having an isotactic pentad fraction of 98 % or more, and the copolymer portion containing propylene at 45 to 85 % by weight, and having a glass transition temperature of -40 °C or lower and a weight-average molecular weight of 500,000 to 2,000,000: 30 to 95 % by weight, and ethylene- or styrene-based elastomer having an MFR of 0.1 to 20 g/10 minutes and a density of 0.850 to 0.910 g/cm 3: 5 to 50 % by weight, supplying carbon fibers as the following component:: carbon fibers having a fiber diameter larger than 2 μm, but 15 μm or less and a fiber length of 1 to 20 mm: 0.5 to 20 % by weight, through a side feeder into the components and being molten and kneaded to disperse the carbon fibers and control the breaking of the carbon fibers to an average length of 0.05 mm or more, but below 20 mm, and extruding the resulting polypropylene-based resin composition into pellets or a molded shape.: propylene block copolymer having an MFR of 50 to 150 g/10 minutes and composed of a propylene homopolymer portion and a copolymer portion of propylene and another α-olefin, the propylene homopolymer portion having an isotactic pentad fraction of 98 % or more, and the copolymer portion containing propylene at 45 to 85 % by weight, and having a glass transition temperature of -40 °C or lower and a weight-average molecular weight of 500,000 to 2,000,000: 30 to 95 % by weight, and ethylene- or styrene-based elastomer having an MFR of 0.1 to 20 g/10 minutes and a density of 0.850 to 0.910 g/cm 3: 5 to 50 % by weight, supplying carbon fibers as the following component:: carbon fibers having a fiber diameter larger than 2 μm, but 15 μm or less and a fiber length of 1 to 20 mm: 0.5 to 20 % by weight, through a side feeder into the components and being molten and kneaded to disperse the carbon fibers and control the breaking of the carbon fibers to an average length of 0.05 mm or more, but below 20 mm, and extruding the resulting polypropylene-based resin composition into pellets or a molded shape.