In view of the fact that the wavelet packet transform (WPT) can only weakly detect the occurrence of fault, this paper applies a fault diagnosis algorithm including wavelet packet transform and principal component analysis (PCA) to the inverter-side fault diagnosis of multi-terminal hybrid high-voltage direct current (HVDC) network, which can significantly improve the speed and accuracy of fault diagnosis. Firstly, current amplitude and current slope are used to sample the data, and the WPT is used to extract the energy spectrum of the signal. Secondly, an energy matrix is constructed, and the PCA method is used to calculate whether the squared prediction error (SPE) statistics of various signals that can reflect the degree of deviation of the measured value from the principal component model at a certain time exceed the limit to judge the occurrence of the fault. Further, its maximum value is compared to determine the fault types. Finally, based on a large number of MATLAB/Simulink simulation results, it is shown that the PCA method using the current slope as the sampled data can detect the occurrence of a ground fault with small transition resistance within 2 ms, and identify the fault types within 10 ms, without being affected by the sampling frequency.