The present invention provides a curable composition capable of giving rubbery cured products having excellent adhesion properties to all-purpose substrates, improved weather-resistant adhesion properties to photocatalyst-coated transparent adherends, low modulus and high elongation and, further, showing high weather resistance without undergoing surface cracking or discoloration even when used outdoors for a long period of time. The curable composition of the present invention includes a vinyl polymer (I) and an antioxidant (II). A main chain of the vinyl polymer (I) is a product of living radical polymerization, and the vinyl polymer (I) contains at least one crosslinkable silyl group.