Although the floating slab track (FST) is an effective way to isolate the vibration transmitted to infrastructure, the track’s stiffness varies periodically in space due to the periodic installation and discontinuity of floating slabs. This will lead to a parametric excitation vibration when a train is moving over the track at certain speed. In order to make an investigation into this issue, a vehicle-floating slab track coupling model is developed in the time domain and a solution based on the modal superposition method is proposed. Then the parametric excitation vibration of FST and its factors are studied using this model. It is found that the main frequency components of such vibration are the floating slab passing frequency and its multiples. With the train speeding up or the natural frequency of the floating slab isolation system decreasing, the wheel/rail dynamic interaction force increases, and its peak-to-peak value is about 75% of the static wheel/rail load when the vehicle runs over the FST with natural frequency of 10 Hz or 6 Hz at a speed of 60 m/s. Whereas there exists a critical value of the single slab length, which corresponds to the larger wheel/rail dynamic interaction force as the single slab length changes. Moreover, adjusting the installation location and the stiffness of slab bearings within unit slab can decrease the track stiffness variation. As a result the wheel/rail dynamic load from the parametric excitation vibration decreases.