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Multiple-chip packaging becomes common in LEDs packaging community. For such types of packaging, thermal spreading resistance is an important factor to impact the total thermal performance of LEDs. In this paper, a general analytical solution based on the method of variable separation for thermal spreading resistances of eccentric heat sources on a rectangular flux channel is used to calculate the whole temperature field of LED packaging substrate. The feasibility of the analytical method used in LEDs packaging has been proven by the temperature comparison with existing experimental results of an 80 W LED street lamp. According to the analytical solution, optimization analysis is presented in order to obtain more uniform temperature distribution on the substrate of the multi-chip LEDs packaging. The optimization results can effectively instruct the LED packaging design and reduce the system thermal resistance.