By studying the correlativity between energy, volume and electronic structure of characteristic crystals and bound conditions of OA theory, the potential energy function, atomic volume interactive function and electronic structure of Au-Cu alloys have been determined. Then following the general Vegard's law in characteristic theory,the electronic structure and properties of disordered continue solid solution and three ordered alloys with the maximum ordering degree are calculated. It is found that the non-bonding electrons and near-free electrons in outer shell will transform to covalent electrons during alloying. By analyzing the variation of electronic structure and cohesion of ordering and disordered alloys, the transformation of order-disorder transition Au-Cu alloy has been studied.