In this study, a railway suspension bridge is modeled as a suspended beam and the train over it as a sequence of moving sprung masses. To investigate the bridge response subjected to simultaneous actions of moving load and earthquake-induced support motions, the total response of the suspended beam under ground motions can be decomposed into two parts: the pseudo-static response and the inertia-dynamic component, in which the pseudostatic displacement is analytically obtained by exerting the support movements on the suspended beam statically and the governing equations in terms of the inertia-dynamic component as well as moving oscillators are transformed into a set of nonlinearly coupled generalized equations by Galerkin's method. When conducting the dynamic response analysis of a suspended beam subject to moving vehicles and multiple support excitations, one needs to deal with nonlinear coupling vibration problems with time-dependent boundary conditions. Instead of solving the coupled equations for the inertia-dynamic generalized system containing pseudo-static support excitations and moving oscillators, this study treats all the nonlinear coupled terms as pseudo forces, and then solves the decoupled equations using Newmark's beta method with an incremental-iterative approach that can take all the nonlinear coupling effects into account. Numerical investigations demonstrate that the present solution technique is available in conducting the dynamic interaction problem with support excitations. Moreover, non-uniform seismic inputs may amplify the both responses of the suspended beam and moving vehicles over it significantly. Such an effect is often neglected by the assumption of uniform seismic ground motions in conventional design of bridge structures.