To effectively evaluate the influence of base-isolation on the dynamic stability of liquid storage tanks, from fluid-solid coupling equations with displacement-pressure form, the perturbation equations with periodic coefficients were established by considering the shell stress stiffening (softening) effects due to hydrostatic and hydrodynamic pressure, the dynamic instability regions were then calculated based on Floquet theory. Taking an 160,000 m3 LNG storage tank for example, the parametric dynamic stability analysis were executed under 2 liquid storage levels and 9 groups of isolation parameters, and 3 suggestions for isolation control were proposed combined with the seismic fortification requirements. The results show that, hydrostatic pressure and stiffening girder can effectively inhibit the expansion of dynamic instability regions, the dynamic instability regions migrate to the low frequency zones with the decrease of isolator stiffness, and the critical instability amplitudes grow with the increase of isolator damp coefficient, and the inhibitory effect of isolator on dynamic instability regions is more significant in half-filled liquid condition than in the full-filled condition.