From the perspective of environmental protection, the permanence and stability are important characteristics of ecosystems. However, it is inevitable that external factors have influence on ecosystems, so it is important for us to study theoretically the stability of an ecosystem under the condition of feedback control. In this paper, we firstly propose a nonautonomous discrete Lotka-Volterra competitive system with a single feedback control. Furthermore, by utilizing the standard comparison theorem and the differential mean value theorem, we obtain the sufficient conditions for the permanence and global attractivity of the system. Finally, a numerical example shows the feasibility of our main results.