The recovery voltage of fault phase includes frequency component and free oscillation component when single-phase grounding transient fault occurs, and only fundamental frequency component when permanent grounding fault occurs. In order to distinguish the transient fault and permanent fault, a new criterion based on Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) was proposed in this paper. ESPRIT algorithm based on subspace rotational invariance techniques to estimate the signal parameters can accurately estimate the frequency and amplitude of the signal. When transient fault occurs, there are two spectral lines of free oscillation component and fundamental frequency component, while when permanent fault occurs, only a spectral line of the fundamental frequency component. The simulation results show that ESPRIT algorithm can accurately estimate the frequency and amplitude of the signals, and the proposed criterion can effectively distinguish between the transient fault and the permanent fault.