Because of the poor accuracy of the commonly used Boltzmann plot method and double-line method, the Boltzmann-Maxwell distribution combined with the Saha-Eggert formula is proposed to improve the measurement accuracy of the plasma temperature;the simple algorithm for determining the linewidth of the emission line was established according to the relationship between the area and the peak value of the Gaussian formula, and the plasma electron density was calculated through the Stark broadening of the spectral lines;the method for identifying the plasma local thermal equilibrium (LTE) condition was established based on the McWhirter criterion. The experimental results show that with the increase in laser energy, the plasma temperature and electron density increase linearly;when the laser energy changes within 127～510 mJ, the plasma electron density changes in the range of 1.305 32×1017～1.873 22×1017 cm-3, the plasma temperature changes in the range of 12 586～12 957 K, and all the plasma generated in this experiment meets the LTE condition threshold according to the McWhirter criterion. For element Al, there exist relatively few observable lines at the same ionization state in the spectral region of the spectrometer, thus it is unable to use the Boltzmann plane method to calculate temperature. One hundred sets of Al plasma spectra were used for temperature measurement by employing the Saha-Boltzmann method and the relative standard deviation (RSD) value is 0.4%, and compared with 1.3% of the double line method, the accuracy has been substantially increased. The methods proposed can be used for rapid plasma temperature and electron density calculation, the LTE condition identification, and are valuable in studies such as free calibration, spectral effectiveness analysis, spectral temperature correction, the best collection location determination, LTE condition distribution in plasma, and so on.