Aiming at the problem of waveform peaking caused by improper range setting in partial discharge detection by the high-frequency pulse current method, this paper proposes a nonlinear least squares fitting algorithm based on the double exponential pulse function model. In this study, a double-exponential impulse function model is established to describe the time-domain characteristics of partial discharge. The Levenberg-Marquardt algorithm is combined to optimize parameter estimation, and a weighting strategy and physical constraints are introduced to improve the fitting stability. Experiments show that the fitting results of this algorithm perform well in parameter indicators such as mean square error and correlation coefficient, and can effectively restore the amplitude and time-frequency characteristics of the truncated waveform. Further verified through the comparison of PRPD spectra, the fitted spectra maintained the phase-amplitude distribution pattern of the original discharge type. When this method was applied to the pattern recognition of convolutional neural networks, the recognition accuracy of high-voltage metal spike defects increased from 35.59% to 95.38%, confirming the engineering application value of this method in improving the reliability of partial discharge diagnosis.