A population inversion study of GaAs/AlxGa1-xAs three-quantum-well quantum cascade structures is presented. We derive the population inversion condition (PIC) of the active region (AR) and discuss the PICs on different structures by changing structural parameters such as the widths of quantum wells or barriers in the AR. For some instances, the PIC can be simplified and is proportional to the spontaneous emission lifetime between the second and the first excited states, whereas some other instances imply that the PIC is proportional to the state lifetime of the second excited state.