Laser-induced breakdown spectroscopy analysis technology is a powerful method for analyzing material composition, but the use of it for quantitative analysis has the disadvantages of inaccurate analysis results and low reproducibility. In order to predict the composition information of olivine in nature accurately, this paper made 15 samples according to the composition information of olivine in nature, and 11 of them were used as standard samples, and the other 4 samples were used as test samples for LIBS quantitative analysis. Lastly, the laser-induced breakdown spectroscopy database of olivine was established with 50 spectra per sample. Then, the multiple linear regression algorithm and the back-propagation algorithm were used to analyze the 50 sets of data of this series of samples, which effectively reduced the inaccuracy of the test results caused by random errors. In the study of the content of forsterite and fayalite in olivine using back-propagation algorithm with data of laser-induced breakdown spectroscopy, the final results showed that the coefficient of determination of the prediction result was 0.901, close to the 0.911 which was yielded with conventional multiple linear regression algorithm. This indicated that the backward propagation algorithm’s prediction accuracy for olivine content was close to the multiple linear regression algorithm. Furthermore, the root mean square error of the result obtained with back-propagation algorithm was 28.64, which was better than the latter’s 29.23, which indicated that the result distribution obtained by the back-propagation algorithm was more concentrated. In addition, by analyzing the correspondence between the size of each numerical value in the correlation matrix and the position of each element’s spectral line, the results showed that the correlation matrix F inverted with back-propagation algorithm had a higher correlation with the physical meaning represented by it. This showed that the performance of the back-propagation operation was comparable to that of the traditional multiple linear regression algorithm, and it performed better in predicting the consistency of the data. In addition, the back-propagation algorithm could directly analyze the data of the olivine full spectrum data obtained by laser induced breakdown spectroscopy without the step of spectral peak finding, simplifying the process of data analysis and making up the shortcomings of the multiple linear regression algorithm in analyzing full-spectrum data.