A design method for light-emitting diode (LED) array is proposed to achieve a good uniform illumination distribution on target plane. By using random walk algorithm, the basic LED array modules are optimized firstly. The optimized basic arrays can generate uniform illumination distribution on their target plane. The optimized basic LED array modules can be integrated into a large LED array module with more than tens of LEDs. In the large array, we can select a sub-array with K LEDs (K>7), which can produce the good uniform illumination distribution. By this way, we design two LED arrays which consist of 21 and 25 LEDs, respectively. The 21-LED array and 25-LED array can generate uniform illumination distributions with the uniformities of 95% and 90%, respectively.