The traveling wave signals（TWS） are weak when the voltage is near the zero-cross point or the high resistance grounded fault occurs. Besides， they may be distorted and disturbed by noise as well. In such a case， the singularity point of TWS may not be detected correctly with traditional wavelet transformation detection method， so a novel singularity point detection method for weak TWS is proposed. The basic principle of the method is to detect the singularity point with the fitted curve of faulty TWS. The fitted curve is determined by integration of the expression for traveling wave front（TWF） with the real-time measuring data of high-speed acquisition units. After the characteristic analysis of rising edge of TWF and influence on rising edge of TWF caused by distributed capacitance on bus bar， the expression for rising edge of TWF is deduced. Furthermore， in order to improve the feasibility of the algorithm， TWF indirect expression is deduced with Maclaurin expansion. TWS singularity point can be detected from the fitted curve based on the indirect expression. The simulation results show the validity of this method.