In terms of the power quality data reconstruction with the compressed sensing principle, the orthogonal basis generated by normal function cannot be used to obtain the best sparse representation. Therefore, the K-Singular Value Decomposition (K-SVD) dictionary is applied to the power quality data reconstruction for the first time. First of all, the power quality signals are converted from One-Dimensional (1D) to Two-Dimensional (2D) and then overcomplete dictionary adaptable for power quality signals is established, which is based on the K-SVD dictionary. Meanwhile compressed sampling is carried out for power quality disturbance signals by taking the Gauss random matrix as the measurement matrix. In addition, 2D reconstruction is conducted for the signals with the Compressed Sensing Matching Pursuit (CoSaMP) algorithm, and 2D signals are converted to 1D signals. Finally, simulation verification is implemented for several common power quality signals with new algorithm. Experiment result shows that at the compression ratio of 25%, the new algorithm can be used to complete the reconstruction of the signals with signal-to-noise ratios more than 44.2 dB, which meets the analysis requirements in practical application. This work is supported by Natural Science Foundation of Jilin Province (No. 20140101066JC).