The invention is to provide an aqueous dispersion having good adhesiveness, especially airtight adhesiveness to various substrates, and having good storage stability, good weather resistance and good hydrophobicity. The aqueous dispersion comprises a block copolymer composed of polymer blocks (A) consisting essentially of olefin monomer units and polymer blocks (B) comprising from 2 to 100 mol % of units of vinyl monomers having a carboxyl group or a carboxylic acid anhydride group and from 0 to 98 mol % of units of other vinyl comonomers capable of copolymerizing with the vinyl monomers, dispersed in an aqueous solution of at least 0.05 equivalents, relative to the carboxyl group or the carboxylic acid anhydride group, of a basic substance.