The rapid development of modern society makes cables reach into every corner of human society. An urgently unsolved problem is to ensure cable line running safely for longtime. Thist is a new and hot field in our country to monitor cable insulation state and to diagnose cable fault accurately on line so the topic has an exigently realistic significance. The methods of cable fault location, fault recognition, system modeling, information fusion, are researched deeply based on the theories of wavelet and neural network after the domestic and international currently states of cable fault diagnoses are summarized. The main research works of this dissertation consist of the following parts.For the problem that the uncertainty of traveling wave speed influences the precision of fault location, the Central Distance Theorem is presented after three new concepts of Layer Time, Layer Wave Speed, and Central Distance are defineded based on the theory of Wavelet analysis. Then the proof of the Central Distance Theorem is given. The marching relation between traveling wave time and traveling wave speed is built. The disturbances on the precision of fault location from the other frequencies components are eliminated. According to the Central Distance Theorem, the Inference 1 and Inference 2 of the Central Distance Theorem are obtained. That is the cable fault location method of impulse currents difference and the cable fault location method of zero-order variable difference. These two methods can find the accurate distance of cable fault. Simutaniously, the two methods solve the problem of blind distance and the problem of being difficult to identify fault signals which are easy to be confused by cable joints or other uneven dielectric points. Simulations show that the fault location errors by the Central Distance Theorem and the Inference 1 and the Inference 2 are much smaller than that by the commen used traveling wave method.Aiming at the problem of cable fault recognition, a method of cable fault recognition by