Laser-induced breakdown spectroscopy (LIBS), an element-detection technology with the advantages of no sample preparation and in situ detection of metal samples, is suitable for the quantitative analysis of metal samples. However, severe spectral interference in the detection of metal samples makes the quantitative analysis difficult. Three quantitative analysis methods, including single-variable calibration, partial least squares regression (PLSR), and support vector regression (SVR), are used to conduct the quantitative analysis of four common metal elements (Manganese (Mn), Chromium (Cr), Vanadium (V), and Titanium (Ti)). The PLSR model adds interference spectrum lines to the model for linear modeling, while the SVR model adds interference spectrum lines to the model for nonlinear modeling. The quantitative analysis results of the nonlinear SVR model are the best. The R square (R2) values of Mn, Cr, V, and Ti are 0.993, 0.995, 0.990, and 0.992, respectively. The root-mean-squared errors of the prediction set of Mn, Cr, V, and Ti are 0.044, 0.045, 0.011, and 0.014, respectively. Therefore, the results of PLSR and SVR are better than the calibration curves of the spectral intensity and concentration due to the influence of multivariate factors. SVR has almost no element bias, while PLSR and the single-variable calibration model have different quantitative results due to the different degrees of influence on spectral lines. These results demonstrate that the combined influence of the spectral interference, background noise, and self-absorption can be suppressed by the nonlinear quantitative analysis model in the steel field using LIBS.