Let X be a Banach space over the field R or C, a 1 ,...,a p ∈ C, and (b n) n≥0 a sequence in X. We investigate the Hyers-Ulam stability of the linear recurrence x n+p = a 1 x n+p-1 + ••• + a p-1 x n+1 + a p x n + b n , n ≥ 0, where x 0 ,x 1 ,...,x p-1 ∈ X.