With M-shell X-ray radiation from plasma produced by nanosecond high power laser irradiating on high atomic number targets, the experimental study on Si K-edge X-ray absorption near-edge structure (XANES) is carried out with an elliptic cylinder crystal spectrometer. By describing the experiment setup in detail, and analyzing the principle of elliptic cylinder crystal spectrometer, the position-energy dispersion relation of the spectrometer is obtained, and the laser plasma X-ray spectra from six targets of Au, Lu, Yb, Dy, Ta, and Co are compared. The results show that by comparing the laser plasma X-ray spectra from six targets of Au, Lu, Yb, Dy, Ta and Co, we find that the M-shell radiations from Lu, Yb, and Dy are more brilliant than the others in the vicinity of Si K-edge (1839 eV), and the corresponding signal to noise of XANES is much better. The XANES obtained from experiment and calculation by FEFF9.0 software are in good agreement with each other, indicating that the static experimental result of single shot is reliable.