A new simplified parametric model, which is more suitable for pantograph–catenary dynamics simulation, is proposed to describe the nonlinear displacement-dependent damping characteristics of a pantograph hydraulic damper and validated by the experimental results in this study. Then, a full mathematical model of the pantograph–catenary system, which incorporates the new damper model, is established to simulate the effect of the damping characteristics on the pantograph dynamics. The simulation results show that large F const (saturation damping force of the damper during compression) and C (initial damping coefficient of the damper during extension) in the pantograph damper model can improve both the raising performance and contact quality of the pantograph, whereas a large C has no obvious effect on the lowering time of the pantograph; the nonlinear displacement-dependent damping characteristics described by the second item in the new damper model have dominating effects on the total lowering time, maximum acceleration and maximum impact acceleration of the pantograph. Thus, within the constraint of total lowering time, increasing the nonlinear displacement-dependent damping coefficient of the damper will improve the lowering performance of the pantograph and reduce excessive impact between the pantograph and its base frame. In addition, damping performance of the new damper model would vary with the vehicle speeds, when operating beyond the nominal-speed range of the vehicle, the damping performance would deteriorate obviously. The proposed concise pantograph hydraulic damper model appears to be more adaptive to working conditions of the pantograph, and more complete and accurate than the previous single-parameter linear model, so it is more useful in the context of pantograph–catenary dynamics simulation and further parameter optimizations. The obtained simulation results are also valuable and instructive for further optimal specification of railway pantograph hydraulic dampers.