Aiming at the problem of poor recovery of transient power quality data signal based on compressive sensing, this paper proposed the discrete wavelet sparse and the generalized orthogonal matching pursuit(gOMP) in reconstructing power quality data. When transient signals have appeared, the discrete wavelet sparse based can grab the details at that time. Owing to the selection of multiple “correct” indices with no additional post-processing operation, the gOMP algorithm is finished with the much smaller number of iterations when compared to the OMP, and gOMP can reconstruct K sparse power quality signals well. This paper shows that the gOMP can perfectly reconstruct any K-sparse power quality data. This paper also demonstrated by empirical simulations that the gOMP has excellent recovery performance and computational complexity. After a series of experiments, both transient and steady state signals are perfectly reconstructed and reconstruction accuracy is greater than 99.76%, and refactoring time is significantly reduced.