Generation of magneto-hydrodynamic surface wave by a moving oscillatory disturbance in a finite depth ocean bounded below by a horizontal porous bottom is presented. The governing initial-boundary value problem is solved using Laplace-Fourier transform and an integral form of the surface elevation is obtained. The asymptotic solutions for the free surface elevation are obtained using stationary phase method. The results show that both the steady-state and transient components exist where the latter decays asymptotically and steady-state is reached. It is seen that the bottom permeability has a significant impact on surface elevation. The dispersion relation is also taken into account and the phase and group velocities for deep water and shallow water are analyzed for different values of the parameters in number of figures. The results for limiting case in which the current speed and the porosity vanishes are compared with the calculations investigated earlier.