Summary: In this paper, we not only give some properties of \(W_d\)-fuzzy implication algebras which are sub-algebra of fuzzy implication algebras, but also give a necessary and sufficient condition under which an algebra \( (X, \to, 0)\) of type \( (2,0)\) comes to be a \(W_d\)-fuzzy implication algebra. We obtain some interesting results including that any \(W_d\)-fuzzy implication algebra is regular fuzzy implication algebra, but the inverse is not true, and that any \(W_d\)-fuzzy implication algebra must not be commutative fuzzy implication algebra.