With the increasing use of high-frequency power electronic devices in power systems, the phenomenon of supraharmonics in distribution networks has become a new type of power quality problem that needs to be solved urgently. Compared with the huge amount of data generated by the traditional harmonic detection method, when sampling supraharmonics signals, compressed sensing is a new type of signal processing method. After using the measurement matrix to sub-sample the sparse signal to be measured, the original signal can be accurately restored with fewer data through the reconstruction algorithm, which effectively reduces the requirements on the sampling hardware. This paper introduces a supraharmonics measurement method based on a deterministic measurement matrix and VT-SAMP. First, the method uses a measurement matrix constructed from a deterministic random sequence. The structure of this deterministic measurement matrix is easier to transmit and store than a random measurement matrix, and it has the same reconstruction performance as a Gaussian random matrix. Second, aiming at the problem of the sparseness overestimation caused by spectrum leakage in the SAMP algorithm, this paper proposes an improved SAMP algorithm with Variable Threshold (VT-SAMP). It sets a dynamic threshold to control the selection of the inner product in the algorithm and reduce mis-selection in iterations. The improved algorithm enhances the accuracy of supraharmonics measurement and reduces the errors caused by spectrum leakage and noise. Finally, the accuracy and effectiveness of the improved algorithm are proved by simulation and actual measurement results. This work is supported by Youth Science Fund of National Natural Science Foundation of China (No. 51807114).