We study the behavior of all eigenvalues for boundary value problems of fourth-order difference equations Δ 4 y i = λ a i + 2 y i + 2 , − 1 ≤ i ≤ n − 2 , y 0 = Δ 2 y − 1 = Δ y n = Δ 3 y n − 1 = 0 , as the sequence { a i } i = 1 n varies. A comparison theorem of all eigenvalues is established for two sequences { a i } i = 1 n and { b i } i = 1 n with a j ≥ b j , 1 ≤ j ≤ n , and the existence of positive eigenvector corresponding to the smallest eigenvalue of the problem is also obtained in this paper.