Parkinson's disease is a movement disorder of the nervous system caused by the abnormal oscillations in cortical-basal ganglia circuits, and electromagnetic induction plays an important role in neuronal activities. In this paper, a subthalamic nucleus-globus pallidus network model with electromagnetic induction is proposed to analyze the dynamic mechanism of the Hopf bifurcation with the help of the magnetic flux variable. By analyzing the characteristic equations and the stability of the model, the conditions for the occurrence of Hopf bifurcation with time delay are obtained, and numerical simulation verifies the results of theoretical analysis. It is revealed that increasing synaptic transmission delay can induced oscillations. In addition, two-parameter bifurcation analysis shows that the increase of average magnetic flux $k$ has a certain elimination the system oscillation caused by synaptic transmission delay $T$ and synaptic connection weight $W_{CS}$. It is hoped that the results might have some help in understanding the role of electromagnetic induction in Parkinson's disease.