In electricity transmission system, cables are of great significance because of their electrical and mechanical properties. Nevertheless, negative factors such as local breakage defects caused by improper installation may threaten the security of the power system. To avoid serious accidents, the localization and assessment of breakage defect is needed. In this paper, the pseudo Wigner- Ville distribution with Gaussian window is proposed, which can greatly reduce the values of the cross-terms caused by conventional Wigner- Ville distribution. Besides, the numerator of the cross-correlation function between the incident signal and the reflected signal is utilized to assess the degree of the breakage. In experiments, the breakage defects are all located accurately with error rates less than 0.5 % of the whole cable length, and the peak value of the assessment curve at the breakage becomes larger with increasing degree of damage.