Fiber-optic laser-induced breakdown spectroscopy (FO-LIBS), which delivers the laser energy through an optical fiber cable, is more suitable for remote analysis and applying in complex environment than traditional laser-induced breakdown spectroscopy (LIBS). However, since the laser fluence is limited by optical fiber loss and attenuation, FO-LIBS suffers more from spectral interference, matrix effect, and self-absorption effect. In this work, three multivariate quantitative analytical methods, including two linear models partial least squares (PLS) and sparse partial least squares (SPLS), one nonlinear model support vector machine (SVM), were utilized to carry out the quantitative analysis of four trace metal elements (Manganese (Mn), Chromium (Cr), Nickel (Ni), and Titanium (Ti)) in pig iron. And the quantitative analytical ability of linear model and nonlinear model was studied and compared. The results show that nonlinear SVM model has the best performance. Using the SVM model, the coefficients of determination (R2) of Mn, Cr, Ni, and Ti were 0.9705, 0.9849, 0.9882, and 0.9837, respectively, and the root mean squared errors of prediction (RMSEP) of Mn, Cr, Ni, and Ti were 0.0982 wt%, 0.0185 wt%, 0.0179 wt%, and 0.0178 wt%, respectively. This work demonstrates that nonlinear quantitative analytical methods can effectively overcome those nonlinear effects and improve the quantitative analytical accuracy of FO-LIBS