The present study deals with the transient flexural gravity wave motion associated with floating elastic plate in the presence of permeable bottom. Integral form of the floating plate deflection is obtained analytically using Laplace–Fourier transform method and the asymptotic solution is derived for large time using stationary phase method. Also, using fast Fourier transform method the time domain simulation of floating plate deflection is obtained. The effect of current, compressive force and porosity parameter on phase and group velocities and floating plate deflection are analyzed. It is observed that in the absence of current, due to the presence of porosity parameter there exist two points where there is a situation of no wave propagation. It is also observed that the current and compressive force have significant effect on transient flexural gravity wave motion whereas the porosity parameter has small impact on the gravity wave motion associated with floating elastic plate. The properties of the roots of the dispersion relation associated with the flexural gravity wave motion in the presence of permeable bed are discussed analytically and numerically. © 2020, Springer Nature B.V.