A vibration-damping pressure-sensitive adhesive composition containing a crosslinked structure of a copolymer comprising (A) from 75 to 92% by weight of a main monomer comprising an alkyl (meth)acrylate containing from 8 to 12 carbon atoms in the alkyl moiety thereof and (B) from 8 to 25% by weight of a carboxyl-containing monomer whose homopolymer has a glass transition temperature of 50.degree. C. or more, said crosslinked structure having a solvent-insoluble content of 80% by weight or more and a weight loss of 3% by weight or less on heating at 120.degree. C. for 240 hours, and said composition having a T-peel strength of 400 g/20 mm-width or more from a SUS plate and a loss factor of 0.05 or more at 60.degree. C. in the vicinity of 1 kHz as determined by a half-value width method. The composition exhibits satisfactory heat resistance against long-term use in high temperatures as well as satisfactory adhesion to various parts at room temperature.