The magnetohydrodynamic transient free convection flow of a viscous incompressible fluid caused by the sinusoidal oscillation of a plane flat porous plate has been studied in this paper. The constitutive equations of continuity and mass conservation of electrically conducting liquid are obtained in Cartesian co-ordinates. The well known Laplace-transform technique is used to solve the equation. The solution has been obtained in exact form. The answer presented herein contains exponential and error function of complex arguments. These functions are readily available in newer mathematical tables. Graphs of the transient solution are presented for  boundary conditions. Velocity distributions in the fluid are also plotted. It is seen that magnetic parameter (M) and porosity of the plate largely affect the fluid velocity field.