Parkinson's disease (PD) is mainly characterized by changes of firing and pathological oscillations in the basal ganglia (BG). In order to better understand the therapeutic effect of noninvasive magnetic stimulation, which has been used in the treatment of PD, we employ the Izhikevich neuron model as the basic node to study the electrical activity and the controllability of magnetic stimulation in a cortico-basal ganglia-thalamus (CBGT) network. Results show that the firing properties of the physiological and pathological state can be reproduced. Additionally, the electrical activity of pyramidal neurons and strong synapse connection in the hyperdirect pathway cause abnormal $\beta$-band oscillations and excessive synchrony in the subthalamic nucleus (STN). Furthermore, the pathological firing properties of STN can be efficiently suppressed by external magnetic stimulation. The statistical results give the fitted boundary curves between controllable and uncontrollable regions. This work helps to understand the dynamic response of abnormal oscillation in the PD-related nucleus and provides insights into the mechanisms behind the therapeutic effect of magnetic stimulation.