A curable composition comprising (A) an organic polymer having a reactive silicon-containing group, and (B) a block copolymer containing in its molecule one soft segment and at least one hard segment having structural units of an aromatic vinyl monomer. The composition has an improved adhesive property to substrates to which conventional curable compositions comprising an organic polymer having a reactive silicon-containing group are hard to adhere, such as mortar, concrete, fluorocarbon resin coats, EPDM rubber sheet, polyvinyl chloride resin sheet and acrylic resin substrate.