By considering the random disturbances caused by the low- frequency internal excitation of torque fluctua-tion,damping ratio,gear backlash,meshing frequency and meshing stiffness,the random vibration equations of asingle pair of spur gear system with three degrees of freedom are established based on Newton's law.Then,the mo-tion differential equations are solved by means of the Runge- Kutta method,and the bifurcation and stability of thegear system with varying gear meshing frequency are analyzed according to the bifurcation diagram,phase diagram,time course diagram and Poincaré mapping graph of the system.Finally,the effect of the random disturbance ofmeshing frequency on the system dynamics is investigated.Numerical simulation results show that (1) there existsabundant period- doubling bifurcation in the random non- smooth gear system; (2) with the decrease of meshing fre-quency,the periodic motion of gear system becomes chaotic via the period- doubling bifurcation; (3) by eliminating6 unstable speed sections,a stable speed section can be obtained in a dimensionless meshing frequency range from0.1 to 6.0; and (4) as the system motion is extremely sensitive to the random disturbance of meshing frequency,the influence degree should be taken into consideration during the system modeling.