A dynamic model of a pantograph-catenary system is established. In the model, motion of the pantograph is coupled with that of the catenary by friction. Stability of the pantograph-catenary system is studied using the finite element complex eigenvalue method. Numerical results show that there is a strong propensity of self-excited vibration of the pantograph-catenary system when the friction coefficient is greater than 0.1. The dynamic transient analysis results show that the self-excited vibration of the pantograph-catenary system can affect the contact condition between the pantograph and catenary. If the amplitude of the self-excited vibration is strong enough, the contact may even get lost. Parameter sensitivity analysis shows that the coefficient of friction, static lift force, pan-head suspension spring stiffness, tension of contact wire, and the spatial location of pantograph have important influences on the friction-induced, self-excited vibration of the pantograph-catenary system. Bringing the friction coefficient below a certain level and choosing a suitable static lift force can suppress or eliminate the contact loss between the pantograph and catenary.