This paper presents wavelet analysis and statistical techniques for assessing the insulation condition of power cables. A specific fault is made and placed on the terminal joint of a 25 kV power cable, and the deterioration phenomena is accelerated by the overvoltage method. The deterioration phenomena of the internal insulation material are explained by wavelet analysis and statistical techniques using partial discharge (PD) current pulse waveforms. The PD value reaches its maximum level, and average discharge level rises, before insulation breakdown. However, the discharge numbers and the equivalent time-length of partial discharge current pulse waveforms fall, causing a current pulse with a large amplitude, and a short time period in the final stage of PD. The proposed method is demonstrated to be effective and feasible.