To make the superconducting magnetically levitated (maglev) transport system more attractive, it has been important to enhance the ride comfort by controlling vehicle vibration. We have reduced maglev vehicle vibration by controlling only the secondary suspension between the car bodies and bogies. However, by doing so, it has been difficult to reduce vibration for the characteristic and relatively high frequencies of the primary suspension. Recently, we have directed our attention to primary suspension control, using power collection coils of the distributed-type linear generator system, which we are testing as an onboard power source. Because this type of vibration control can apply damping directly to the primary suspension, we consider it to be optimal for reducing vibrations at high frequencies. We have used maglev vehicle models that focus on lateral, vertical, rolling, and pitching motions to describe the effectiveness of reducing vibrations by using linear generator system damping force control in the primary suspension and linear quadratic (LQ) control of the actuators in the secondary suspension.