Compared with the plane target surface, it is more complex for designing light emitting diode (LED) array to produce a uniform illumination distribution on the curved surface. In this paper, the uniform illumination distribution in curved target surface is produced by optimizing the LED array arrangement. In the optimization, firstly, the objective function is constructed to reflect the uniformity of illumination distribution. The objective function takes the coordinates of each LED in the array as variables. Then, the location coordinates of each LED in the array is optimized by simulated annealing algorithm, so that the objective function is minimization. In order to verify the feasibility of the algorithm, we design the cylindrical curved surface, parabolic and sinusoidal curved surface as target surfaces. With the three different kinds of target surfaces, three different LED array arrangements are designed. The three arrays produce uniform illumination distribution on the corresponding target surfaces with the uniformity of 99.0%, 99.3% and 97.0%, respectively. The influence of assembly tolerance of LED arrays on the illumination uniformity of the target surface is also analyzed. The simulation results show that the decrease of the uniformity is no more than 0.3% when the assembly tolerance is within 0.2 mm. This indicates that the design method has good practical value.