Abstract: The vibration of Terfenol-D rod, which is the key structure element in magnetostrictive actuator, is investagated with initial condition. The vibration of rod is excited by input harmonic alternating current and the initial state of rod is at rest. As the standard square constitutive relation is employed, the coefficients in governing equation and boundary conditions become variable with time. The approximate analytic solution of displacement response which is excited by harmonic alternating current can be derived by means of perturbation method, since the mathematical model of the problem has a small parameter. The computational results show that the displacement response is periodic and reveals the characteristic of frequency doubling under low frequency current. Finally, the influence of magnetostriction and current parameters on the displacement response is investigated.