The cognitive impairment will gradually appear over time in Parkinson's patients, which is closely related to the basal ganglia-cortex network. This network contains two parallel circuits mediated by putamen and caudate nucleus, respectively. Based on the biophysical mean-field model, we construct a dynamic computational model of the parallel circuit in the basal ganglia-cortex network associated with Parkinson's disease dementia. The simulated results show that the decrease of power ratio in the prefrontal cortex is mainly caused by dopamine depletion in the caudate nucleus and is less related to that in the putamen, which indicates Parkinson's disease dementia may be caused by a lesion of the caudate nucleus rather than putamen. Furthermore, the underlying dynamic mechanism behind the decrease of power ratio is investigated by bifurcation analysis, which demonstrates that the decrease of power ratio is due to the change of brain discharge pattern from the limit cycle mode to the point attractor mode. More importantly, the spatiotemporal course of dopamine depletion in Parkinson's disease patients is well simulated, which states that with the loss of dopaminergic neurons projecting to the striatum, motor dysfunction of Parkinson's disease is first observed, whereas cognitive impairment occurs after a period of onset of motor dysfunction. These results are helpful to understand the pathogenesis of cognitive impairment and provide insights into the treatment of Parkinson's disease dementia.