Parkinson's disease (PD) is characterized by abnormal beta oscillations (13-30 Hz) within the basal ganglia, which contribute not only to motor symptoms but also to sleep disturbances. In this study, we developed a computational model of the basal ganglia-thalamocortical (BGTC) network that includes the pedunculopontine nucleus (PPN), to investigate the mechanism by which the abnormal oscillations disrupt sleep. The model incorporates key nuclei, neurotransmitter systems, and neural pathways to simulate sleep-related brain activity in Parkinsonian conditions. Our simulations show that abnormal beta oscillations impair sleep across all vigilance states. During wakefulness, elevated beta activity in the basal ganglia and cortex prolongs sleep latency. In rapid eye movement (REM) sleep, reduced firing in the pedunculopontine nucleus combined with enhanced beta oscillations underlies features of REM sleep behavior disorder (RBD). In Non-REM 2 (N2) sleep, the formation of sleep spindles is reduced and shifted toward higher frequencies, promoting sleep fragmentation. In Non-REM 3 (N3) sleep, slow-wave amplitude decreases, indicating reduced depth. Propagation analysis reveals that the neural pathways Lhx6-cortical inhibitory neurons (IN), PPN-thalamic reticular nucleus (RE), and globus pallidus internus (GPi)-thalamocortex (TC) can facilitate the propagation of beta oscillations to cortex, while the GPi-TC pathway suppresses it during wakefulness, REM, and N2 sleep. Additionally, the pathway Lhx6-cortical pyramidal neurons (PY) inhibits beta propagation during wakefulness but promotes it during other sleep stages. These findings identify specific pathways through which abnormal beta oscillations propagate and disrupt thalamocortical sleep rhythms, providing new insights into the mechanisms underlying sleep disturbances in Parkinson's disease and highlighting potential therapeutic targets.