A nonlinear four degrees-of-freedom mathematical model is created with considering the normal and tangential vibration of friction interface based on pin-on-disc friction system. The influences of normal and tangential damping in system's stability are investigated respectively， based on complex eigenvalue analysis and time-domain analysis. Results of complex eigenvalue analysis show that the critical friction coefficient for the generation of unstable is strongly affected by damping. An optimal damping ratio has been found to make the system exhibits best performance of stability. Further numerically simulation shows that an appropriate choosing of damping ratio and larger values of tangential and normal damping can extremely increase the stability of system and reduce the tendency of unstable vibration of friction system. Additionally， taking stick-slip phenomenon into consideration， the numerical simulation in time domain has been calculated. The results indicate that the system behavior of vibration will successively come through three phases： slip stage with the increasing of amplitude， stick-slip stage with the increasing of amplitude and the stick-slip stage. Both the tangential and normal damping will influence the stick time， and the tangential and normal amplitudes of limit cycles.