The Cu content in pig feed is quantitatively analyzed based on the single pulse laser-induced breakdown spectroscopy (LIBS), where the intensities of two characteristic spectral lines of Cu at the wavelength of 324.74 nm and Ca at the wavelength of 317.95 nm are used as the independent variables for the multi-variable nonlinear regression, and the Cu content in feed is used as the dependent variable. The analysis results from the single variable method, the cross dimension-reduction nonlinear multi-variable approximation model, the nonlinear multi-variable quadric model and the square dimension-reduction nonlinear multi-variable approximation model are compared, and the samples for validation are predicted and analyzed. The results show that the cross dimension-reduction nonlinear multi-variable approximation model has the best prediction performance than the other methods in which the fitting correlation coefficient between the predicted concentration and the actual concentration is 0.9799 for the modeling set and 0.8597 for the prediction set, and the average relative error is 8.12%.