Abstract: In this paper, the strong product of two fuzzy graphs is defined. It is proved that when two fuzzy graphs are effective then their strong product is always effective and it is proved that the strong product of two complete fuzzy graphs is complete. Also it is proved that the strong product of two connected fuzzy graphs is always connected. The lower and upper truncations of the strong product of two fuzzy graphs are obtained. The degree of a vertex in the strong product of two fuzzy graphs is obtained. A relationship between the direct sum and the strong product of two fuzzy graphs is obtained.