Using Monte Carlo method to study the magnetic training effect in the ferromagnetic/antiferromagnetic bilayers, it was shown that the magnetic relaxation of the net magnetization induced by cold magnetic field which exists in the interface between ferromagnetic and antiferromagnetic bilayer can result in the training effect in the exchange bias and coercivity of the system. Further studies have shown that the doping in antiferromagnetic layer can modulate the training effect in the exchange bias, because the doping in antiferromagnetic layer can effectively change the magnetic relaxation process of the net magnetization induced by the cold field.