The exchange bias of bilayer magnetic films consisting of ferromagnetic (FM) and antiferromagnetic (AFM) layers in an uncompensated case is studied by use of the many-body Green's function method of quantum statistical theory.The effects of the layer thickness and temperature and the interfacial coupling strength on the exchange bias HE are investigated. The dependence of the exchange bias HE on the FM layer thickness and temperature is qualitatively in agreement with experimental results. When temperature varies, both the coercivity HC and HE decrease with the temperature increasing. For each FM thickness, there exists a least AFM thickness in which the exchange bias occurs,which is called pinning thickness.