In the laser-induced breakdown spectroscopy (LIBS) quantitative analysis technique, the baseline is an important part of the LIBS signal. Due to the fluctuation of laser energy and inhomogeneity of sample surfaces, the phenomenon of plasma emission line drift is obvious. Thus, baseline correction is an essential part during the spectrum data preprocessing. However, the existing algorithms do not have adaptability, thus there usually needs to set some key parameters, such as the suitable fitting function and order. In this paper, baseline correction and spectral signal denoising method are proposed on the basis of the data characteristics, such as the independence and sparsity of the spectral peak as well as the low-pass signal feature of baseline, which forme non-parametric baseline correction model under convex optimization framework. Meanwhile, efficient iterative algorithm is used to ensure the convergence of the results. In this paper, the spectral signal of 23 high alloy steel samples was firstly calibrated, and then the Cr element in the samples of alloy steel was analyzed. Subsequently, 11 analytical lines were selected for quantitative analysis. To verify the effectiveness of the proposed method, we utilized partial least squares (PLS) and support vector machine (SVM) quantitative model for training and prediction respectively. Compared with the traditional methods, the proposed method has a better performance in improving the quantitative analysis accuracy.