We study the asymptotic behavior of the solutions for the following nonlinear difference equation x n + 1 = ∑ i = 1 s A k i x n − k i / ( B 0 + ∑ j = 1 t B l j x n − l j ) , n = 0 , 1 , … , where the initial conditions x − r , x − r + 1 , … , x 1 , x 0 are arbitrary nonnegative real numbers, k 1 , … , k s , l 1 , … , l t are nonnegative integers, r = max { k 1 , … , k s , l 1 , … , l t } , and A k 1 , … , A k s , B 0 , B l 1 , … , B l t are positive constants. Moreover, some numerical simulations to the equation are given to illustrate our results.