Abstract: In this paper, the direct sum of two fuzzy graphs G1 and G2 is defined. It is proved that when two fuzzy graphs are effective then their direct sum need not be effective. The degrees of the vertices in the direct sum of two fuzzy graphs G1 and G2 in terms of degrees of the vertices in the fuzzy graphs G1 and G2 are obtained. The lower and upper truncations of the direct sum of two fuzzy graphs are obtained. The regular property and connectedness of the direct sum of two fuzzy graphs are also studied.