For FeCr/IrMn bilayers, the exchange bias training effect and the magnetization reversal mechanism are correlated to each other and depend on the composition of the ferromagnetic layer. For high Fe contents, the asymmetric magnetization reversal is observed. During the training effect, both exchange field and coercivity decrease monotonically, suggesting a type I training effect. For low Fe contents, the domain wall depinning takes place for the two hysteresis loop branches. Only exchange field diminution happens in the training effect. The coercivity almost does not change in the process, corresponding to a type II training effect. It is suggested that the motion of antiferromagnetic spins is modified by the magnetization reversal mechanism in the ferromagnetic layer.