Thermal transient measurements of high power GaN-based LEDs with multi-chip designs are presented and discussed. Once transient cooling curve was obtained, the structure function theory was applied to determine the thermal resistance of packages. The measured total thermal resistances from junction to ambient were 19.87 K/W, 10.78 K/W, 6.77 K/W for the one-chip, two-chip and four-chip package, respectively. The contribution of each component to the total thermal resistance of the package can be calculated from the cumulative structure function and differential structure function. The total thermal resistance of multi-chip package is found to decrease with the number of chips due to parallel heat dissipation. Very useful thermal design rule for high power multi-chip LED package is analogized from the experiments. It was found that the effect of the number of chips in a package on the thermal resistance depends on the ratio of partial thermal resistance of chip and that of slug. Thermal resistance for full color multi chip LEDs, where each chip is driven independently, was measured as well and the implication was discussed.