A method for producing an aromatic polysulfone by a polycondensation reaction between an aromatic dihalogenosulfone compound and an aromatic dihydroxy compound is described. The polycondensation reaction is performed in the presence of at least one aromatic end-capping agent; and an amount, p mol, of the aromatic dihalogenosulfone compound, an amount, q mol, of the aromatic dihydroxy compound, and an amount, r mol, of the aromatic end-capping agent have a relationship satisfying formula (S1) below and formula (S2) below: r/(p−q) q   (S2).