This study focuses on an aircraft equipped with a twin-wheel dual-strut nose landing gear to investigate the shimmy stability and control of the nose landing gear during ground taxiing. First, by assuming the airframe as a rigid body and taking into account the torsional, lateral bending, and axial motions of the landing gear, alongside the rigid-body motions of the airframe, a full-aircraft ground taxiing dynamic model is established for the aircraft system featuring the dual-strut nose landing gear. Subsequently, based on the established system dynamic model, a numerical solution method is employed to conduct a shimmy stability analysis. The effects of various factors on the landing gear shimmy, including taxiing speed, aircraft mass, and the moments of inertia of both the nose landing gear strut and the tires, are systematically analyzed. Furthermore, a Proportional-Integral-Derivative (PID) control method is applied to control the landing gear shimmy. Based on the shimmy dynamic equations and the Particle Swarm Optimization (PSO) algorithm, appropriate ranges for the control parameters are determined to suppress the shimmy of the nose landing gear. The suppression performance is then compared with that of a MR shimmy damper. The results indicate that, compared to an aircraft with a single-strut nose landing gear, the dual-strut configuration exhibits a smaller shimmy instability region, thereby inherently suppressing the aircraft shimmy to a certain extent. Within a specific range, a decrease in the moment of inertia of the nose landing gear strut and an increase in the twin-wheel spacing lead to an expansion of the landing gear's shimmy region. Finally, compared to the application of the MR shimmy damper, the PID control strategy proves to be more effective in suppressing the landing gear shimmy.