Thermal transient measurements of high power GaN-based LEDs with multi-chip designs are presented and discussed in the paper. Once transient cooling curve was obtained, the structure function theory was applied to determine the thermal resistance of packages. The total thermal resistance from junction to ambient considering optical power is 19.87 K/W, 10.78 K/W, 6.77 K/W for the one-chip, two-chip and four-chip packages, respectively. The contribution of each component to the total thermal resistance of the package can be determined from the cumulative structure function and differential structure function. The total thermal resistance of multi-chip packages is found to decrease with the number of chips due to parallel heat dissipation. Moreover, an important thermal design rule for high power multi-chip LEDs is analogized from the experiments. With the number of chips increasing, the thermal resistance can be decreased, but the impact will be different with the ratio of partial thermal resistance.