The quantitative analysis models of multiple linear regression, neural network regression and support vector machine regression with laser-induced breakdown spectroscopy are established in this paper. Heavy metal Ni in water selected as research object is tested and comparativly analyzed. The average relative standard deviations of multiple linear regression, neural network regression and support vector machine regression are 7.60%, 4.86% and 2.35%, and the maximum standard deviations are 23.35%, 15.20% and 8.29% respectively, the average relative errors are 25.98%, 10.58% and 2.72%, and the maximum relative errors are 116.47%, 47.38% and 9.89% respectively. Methods and reference data are provided for the further study of fast measurement of tracing heavy metals in water by laser induced breakdown spectroscopy technique.