As a maglev transport route has to cross a region with occasional earthquakes, the train/guideway interaction is an issue of great concern in dominating safety of the maglev system. This paper intends to present a computational framework of interaction analysis for a maglev train traveling over a suspension bridge shaken by horizontal earthquakes. The suspended guideway girder is modeled as a single-span suspended beam and the maglev train traveling over it as a series of maglev masses. Due to motion-dependent nature of magnetic forces in a maglev suspension system, appropriate adjustments of the magnetic forces between magnets and guide-rail require the air gaps be continuously monitored. Thus an on-board hybrid LQR+PID controller with constraint rule base is designed to control the dynamic response of a running maglev mass. Then the governing equations of motion for the suspended beam associated with all the controlled maglev masses are transformed into a set of generalized equations by Galerkin's method, and solved using an incremental-iterative procedure. Numerical investigations demonstrate that when a controlled maglev train travels over a suspended guideway shaken by horizontal earthquakes, the proposed hybrid controller has the ability to adjust the levitation gaps in a prescribed stable region for safety reasons and to reduce the vehicle's acceleration response for ride quality.