In order to control the distribution characteristics of the far-field ring-shaped array, we introduce a new light source to produce adjustable far-field distribution by the method of weight function superposition. It has been shown that, by changing the parameters of the light source, one can obtain far-field with various distribution, including distribution with decrease in spectral intensity of specified rings, distribution with disappearances of specified rings, distribution with different spectral intensity of part of lobes in the continuous rings, distribution with part of the lobes in specified rings disappearing and distribution with some lobes in specified rings being stronger. These results will produce some novel far-field distributions which may provide a new idea for further study concerning about the manipulations of far-field array distribution.