Non-diffracting moire fringes are widely used in the field of precision measurement, and the accuracy of finding the central positions of the fringes is the key to realize high-precision measurement. By analyzing the characteristics of the non-diffracting moire fringe images, a method to seek the central positions of the fringes was proposed. Firstly, two local concentric circle regions, including the central spots, were extracted through the feature of intensity distribution. Secondly, the local concentric ring detection was performed to determine the initial center set. Thirdly, the initial center set was clustered to determine the initial positions of the two spot centers. Finally, the abnormal points were deleted and the more precise positions of the center of the two central spots were obtained by iterative algorithm, realizing the positioning purpose of the two central spots of the non-diffracting moire fringes. Theoretical and experimental results show that the method can determine the center position of two spots at the same time quickly and accurately, and the error is less than 1 pixel.