With the large-scale integration of renewable energy sources and widespread application of high-frequency power electronic devices, the issue of supraharmonics in power systems has become increasingly prominent, which imposes a significant challenge to power quality. To mitigate the impact of spectral leakage and the picket-fence effect on the accuracy of supraharmonic disturbance parameter measurements, and reduce the sampling pressure of supraharmonic signal, this article proposes a supraharmonic measurement method based on windowed compressed sensing (CS) and the orthogonal matching pursuit (OMP) algorithm. The four-term third-order Nuttall window function is integrated into CS technology, where a windowed sparse measurement matrix is constructed to enable windowed compressed sampling of supraharmonic signals. Subsequently, the OMP algorithm is used for frequency estimation of the supraharmonic signals, and the three-spectral-line interpolation technique is applied to reduce the picket-fence effect, improving the accuracy of supraharmonic disturbance frequency, amplitude, and phase measurements. Simulation experiments demonstrate that the proposed algorithm significantly addresses the spectral leakage and the picket-fence effect, effectively reduces the data required for supraharmonic detection, and improves the measurement accuracy while improving noise resistance. In practical experiments, the absolute errors in frequency and amplitude measurement for three sets of supraharmonic components are 0.55, 0.36, and 1.09 Hz and 0.0006, 0.0008, and 0.001 V, respectively, validating the effectiveness and practicality of the proposed method.