The quantitative analysis model of laser-induced breakdown spectroscopy with adaptive kernel is established. Effect of ambient noise and energy jitter in measured density of heavy metals is gradually removed by Lorentz fitting and carbon normalization, and the intensity of plasmas is enhanced by graphite enrichment. Quantitative analysis of laser-induced breakdown spectroscopy based on regression intelligent algorithm of support vector machine is achieved. The average relative standard deviations of lead and copper are 6.4361% and 6.9291%, and the maximum standard deviations are 9.1009% and 8.9280%.The average relative errors of lead and copper are 1.6765% and 1.2478 %, and the maximum relative errors are 5.5759% and 4.2604%. The correlation coefficients of lead and copper are 0.9979 and 0.9997. Methods and reference data are provided for the further study of fast measurement of trace heavy metals in water by laser-induced breakdown spectroscopy.