In this paper we use fixed point method to prove asymptotic stability results of the zero solution of the totally nonlinear neutral difference equation with variable delay∆ x (n) = —a (n) f (x (n — τ (n))) + ∆g (n, x (n — τ (n))).An asymptotic stability theorem with a sufficient condition is proved, which improves and generalizes some results due to Raffoul (2006) , Yankson (2009), Jin and Luo (2009)  and Chen (2013).