The basal ganglia (BG), serving as an intermediate bridge between the cerebral cortex and thalamus, are believed to play crucial roles in controlling absence seizure activities generated by the pathological corticothalamic system. Inspired by recent experiments, here we systematically investigate the contribution of a novel identified GABAergic pallido-cortical pathway, projecting from the globus pallidus externa (GPe) in the BG to the cerebral cortex, to the control of absence seizures. By computational modelling, we find that both increasing the activation of GPe neurons and enhancing the coupling strength of the inhibitory pallido-cortical pathway can suppress the bilaterally synchronous 2-4 Hz spike and wave discharges (SWDs) during absence seizures. Appropriate tuning of several GPe-related pathways may also trigger the SWD suppression, through modulating the activation level of GPe neurons. Furthermore, we show that the previously discovered bidirectional control of absence seizures due to the competition between other two BG output pathways also exists in our established model. Importantly, such bidirectional control is shaped by the coupling strength of this direct GABAergic pallido-cortical pathway. Our work suggests that the novel identified pallido-cortical pathway has a functional role in controlling absence seizures and the presented results might provide testable hypotheses for future experimental studies.