This paper is concerned with the boundedness, persistence, and global asymptotic behavior of positive solution for a system of two rational difference equations xn+1=A+(xn/∑i=1kyn-i),    yn+1=B+(yn/∑i=1kxn-i),  n=0,1,…,k∈{1,2,…}, where A,B∈0,∞,  x-i∈0,∞, and   y-i∈0,∞,  i=0,1,2,…,k.