The basins of attraction and global characters of a time-varying nonlinear gear system are analyzed considering friction and backlash by cell-to-cell mapping method. The basins of attraction and global characters of the system are obtained on different input friction coefficients, time-varying stiffness and exciting frequencies. The evolvement trends of the attractor-basin portraits are studied when these parameters are changed. It is found that the basins of attraction are intertwisted with each other. Results show that the Lyapunov exponent of system chaos is reduced and the global dynamic stability of system is relatively stronger, when the larger friction coefficient is considered.