A numerical study on the propulsive characteristics of a biomimetic foil is done by developing an unsteady linearly-varying strength vortex method. A biomimetic foil is represented as a deforming foil with a tail fin. Present method is verified by comparing the simulated results with results using finite element and finite volume methods. A new boundary condition is imposed by considering the relative rotational velocity, which has not been included in the previous published literature. It is found that the undulation amplitude increases the thrust while maximum thickness is stepping down the thrust. It is also shown that there exists an optimal frequency for maximum thrust generation. It is believed that present results can be used in the investigation of the propulsive characteristics of the biomimetic deforming foil.