In the ceramic production process, the content of Si, Al, Mg, Fe, Ti and other elements in the ceramic raw materials has an important impact on the quality of the ceramic products. Exploring a method that can quickly and accurately analyze the content of key elements in ceramic raw materials is of great significance to improve the quality of ceramic products. In this work, laser-induced breakdown spectroscopy (LIBS) is used for rapid analysis of ceramic raw materials. The chemical element composition and content of ceramic raw materials are quite different, which leads to serious matrix effects. Building an artificial neural network model is an effective way to solve the complex matrix effects, but model training can easily lead to overfitting due to the high number of spectral features and the limited number of samples. In order to solve this problem, we propose a feature extraction method that combines the linear regression (LR) and the sparse and under-complete autoencoder (SUAC) neural network. This LR + SUAC method performs nonlinear feature extraction and dimension reduction on high-dimensional spectral data. The spectral data dimension is reduced from 8188 to 100 through the LR layer, and further reduced to 32 through the SUAC encoding layer. Further, a quantitative analysis model for the elemental composition of ceramic raw materials is established by the combination of LR + SUAC and Back Propagation Neural Network (BPNN). Since the input data dimension and redundant information are greatly reduced by LR + SUAC, the overfitting problem of BPNN is greatly reduced. Experiment results showed that the LR + SUAC + BPNN method obtained the best quantitative analysis performance compared with several other methods in the cross-validation process.