Abstract: In order to obtain divergence feature of light spot of a circular light emitting diode(LED) array, illumination formula, and light spot radius formula and divergence angle formula of a circular LED array were deduced by using single LED illumination formula. The dependence of the divergence angle of a circular LED array on the m value, array radius and target distance were analyzed theoretically by using numerical methods. The change data of divergence angle under three conditions were obtained. The results show that the divergence angle decreases with the increase of m value and array radius. However, the divergence angle increases with the increase of target distance. The results are helpful for the illumination source design with circular LED arrays.