Rapid and precise determination of elemental content in soil is significant for precision agriculture and saline-alkali land remediation. Although Laser-Induced Breakdown Spectroscopy (LIBS) offers advantages of rapid, multi-element simultaneous detection, it is prone to issues of insufficient quantitative accuracy and model overfitting under conditions of complex soil matrix interference and small sample modeling, thereby limiting the model's generalization capability. To overcome these limitations, this study developed a quantitative regression model based on a 1-Dimensional Convolutional Neural Network (1D-CNN). This model directly utilises raw LIBS spectra as input, automatically extracting multi-scale spectral features to predict the contents of Ca, Mg, and Na in soil. 10-fold cross-validation results demonstrate that the CNN model performs exceptionally well across both high and low concentration ranges. For high-concentration samples, R2 ≥ 0.972, while for low-concentration samples, R2 ≥ 0.98. This confirms the model's high accuracy and strong generalization capability in quantitative LIBS analysis of small samples. Its overall performance significantly outperforms comparison models such as Random Forest (RF) and Backpropagation Neural Network (BPNN). Further integration with Gradient-weighted Class Activation Mapping (Grad-CAM) enables feature visualisation, confirming that the model's focus regions align with element-specific spectral lines, indicating physical plausibility. This study provides a high-precision, interpretable modeling approach for quantitative LIBS analysis of small-sample native soils.