This paper is concerned with the following nonlinear difference equation xn+1=∑i=1lAsixn-si/(B+C∏j=1kxn-tj)+Dxn,  n=0,1,…, where the initial data x-m,x-m+1,…,x-1,  x0∈ℝ+, m=max⁡{s1,…,sl,t1,…,tk}, s1,…,sl,t1,…,tk are nonnegative integers, and Asi, B, C, and D are arbitrary positive real numbers. We give sufficient conditions under which the unique equilibrium x̅=0 of this equation is globally asymptotically stable, which extends and includes corresponding results obtained in the work of Çinar (2004), Yang et al. (2005), and Berenhaut et al. (2007). In addition, some numerical simulations are also shown to support our analytic results.