The boundedness and asymptotic behavior of all solutions of the neutral delay difference equation Δ( x n − p nx n−k ) + q nx n−l = 0, n = 0,1,2,…, are investigated, where Δ is the forward difference operator, k,l are positive integers, { P n } is a sequence of real numbers and { q n } is a sequence of nonnegative real numbers. The obtained sufficient conditions improve the existing results in the literature.