In recent years, the researches on primitive exponent of two-colored digraph have gained some achievements. This paper studies a kind of two-colored digraph, matrix theory and graph theory are used to research a two-colored digraph, which indicates color-patch map has only two circles, respectively n-cycle and (mn-1)-cycle, and these two cycles only have two public arcs. It gives the primitive condition of two-circled and two-colored digraph, and upper bound of its primitive exponent, as well as depicts the pole figure of upper bound of its primitive exponent.