A curable composition comprises a reactive silicon group-containing polyoxyalkylene polymer which is obtained by reacting a polyoxyalkylene polymer (A) having a molecular weight distribution of 1.6 or less, a number average molecular weight of 15,000 to 50,000, and 0.8 or more reactive groups, on average, per molecule thereof with an organic compound (B) having in the molecule thereof a reactive silicon group and a functional group capable of reacting with the reactive groups of the polymer (A) in a proportion of 0.8 to 1.5 molecules of the organic compound (B), on average, per molecule of the component (A), a filler (C) and a curing catalyst (D). The composition contains no plasticizer or a small amount of plasticizer.