An analytical model is used to study the wave propagation property in the high-speed railway catenary system subjected to a moving pantograph. The contact and messenger wires are modelling by tensioned cables. The Fourier transform is exploited to find out the solution of the governing equation of the tensioned cable, whose vertical deflection is assumed as the superposition of two waves propagating to opposite sides. Through applying the boundary conditions of a real railway catenary system, the wave propagation model of the catenary system is constructed. The effect of the messenger/contact wire tensions on the wave reflection and transmission at the dropper point is analysed. On the basis of a complete model subjected to a moving load, the wave propagation behaviour in the contact wire is analysed. The results demonstrate that several groups of dominant wave frequencies can be observed from the forward and backward waves under the excitation of a constant moving load. Two significant wave components are introduced by a time-varying moving load due to the Doppler Effect. The effect of the matching between the dominant wave frequencies and the natural frequencies sensitive to the moving load on the contact quality is investigated in combination with a realistic FEM pantograph-catenary model. The results show that the resonance may occur when the dominant wave frequency is consistent to the natural frequency sensitive to the moving load, which can be used to reveal the effect of operation and structural parameters on the current collection quality of a pantograph-catenary system.