A design method of curved light-emitting diode (LED) array is proposed. Based on the principle of light superposition, the LEDs are arranged on the free-form surface, and the LED light-emitting angle is controlled through curvature. Based on the analytical formula of off-axis illumination distribution of the LED curved array, a particle swarm optimization algorithm is introduced based on simulated annealing, the constraint conditions are set, a uniformity evaluation function is constructed, and the numerical model of LED curved array is optimized. A physical light source is produced for the illuminance measurement and the defect detection. Both the theoretical simulation and the real detection show that when the inclination angle is 45° and the ratios of the target surface area to the light-emitting surface area are 1∶0.85 and 1∶4,the illumination uniformity is 91.79% and 98.4%, respectively. The results for leather defect detection show that the proposed curved LED array light source can highlight specific defects, quickly and accurately identify defects, and is easy for image processing.