A curable organopolysiloxane composition is provided, which includes (A) an organopolysiloxane containing at least one silicon atom-bonded alkenyl group within each molecule, (B) an organohydrogenpolysiloxane, which contains, within each molecule, at least one silicon atom-bonded hydrogen atom at a molecular chain terminal, and at least two silicon atom-bonded hydrogen atoms at non-terminal positions within the molecular chain, and which satisfies the formula shown below: 0<.alpha./.beta.0.25 (wherein, .alpha. represents the number of silicon atom-bonded hydrogen atoms at non-terminal positions within the molecular chain, and .beta. represents the total number of silicon atoms within the component (B)), in sufficient quantity to provide from 0.1 to 5 silicon atom-bonded hydrogen atoms per silicon atom-bonded alkenyl group within the component (A), and (C) a platinum-based catalyst. The composition can be cured even at low temperatures, generates a cured product that suffers no surface wrinkling, and displays excellent storage characteristics.