Back-propagation neural network combining with laser-induced breakdown spectroscopy (LIBS) are used to calibrate and quantify the contents of Ca and Mg of different kinds of slag. The networks were trained by means of a gradient descent with momentum and adaptive learning rate back-propagation algorithm. The performance of the neural networks with different inputs is studied, so as its predictive performances to be improved, and the effect of the presence of matrix-specific information in the inputs was studied. Higher performance was obtained when the network was fed with one matrix-specific spectral window than only with the areas of selected peaks. The network fed with one matrix-specific spectral window can utilize more information of spectra, and better correct the matrix effect and line interference. The inputs of the neural networks, however, need serious consideration, since they have a good effect on the measurement reproducibility and accuracy.