A nonequilibrium tunneling current through an Anderson impurity system subject to both constant and alternating electric fields is studied. After mapping the time-dependent Anderson Hamiltonian onto a Kondo one (with coupling strength J) we carry out perturbation expansion up to J3, and obtain a remarkably simple analytical expression for the current. The zero-bias anomaly of the dc is suppressed by the ac field. Both the zeroth and the first harmonics are equally enhanced by the Kondo effect, while amplitudes of higher harmonics are relatively small. These results are shown to be valid also below the Kondo temperature.