In Parkinson's disease, the enhanced beta rhythm is closely associated with akinesia/bradykinesia and rigidity. An increase in beta oscillations (12-35 Hz) within the basal ganglia (BG) nuclei does not proliferate throughout the cortico-basal ganglia loop in uniform fashion; rather it can be subdivided into two distinct frequency bands, i.e. the lower beta (12-20 Hz) and upper beta (21-35 Hz). A computational model of the excitatory and inhibitory neural network that focuses on the population properties is proposed to explore the mechanism underlying the pathological beta oscillations. Simulation results show several findings. The upper beta frequency in the BG originates from a high frequency cortical beta, while the emergence of exaggerated lower beta frequency in the BG depends greatly on the enhanced excitation of a reciprocal network consisting of the globus pallidus externus (GPe) and the subthalamic nucleus (STN). There is also a transition mechanism between the upper and lower beta oscillatory activities, and we explore the impact of self-inhibition within the GPe on the relationship between the upper beta and lower beta oscillations. It is shown that increased self-inhibition within the GPe contributes to increased upper beta oscillations driven by the cortical rhythm, while decrease in the self-inhibition within the GPe facilitates an enhancement of the lower beta oscillations induced by the increased excitability of the BG. This work provides an analysis for understanding the mechanism underlying pathological synchronization in neurological diseases. (C) 2017 Elsevier Ltd. All rights reserved.