设$G=(V, E)$ 是简单图, 子集$F\subseteq V$。若由点集$V-F$ 导出的子图不含圈, 则称子集$F$ 是图$G$ 的反馈集。称反馈集的点数的最小值是图$G$ 的反馈数, 用$f(G)$ 表示，即，$f(G)=\min\{|F| : F$ 是图$G$ 的反馈集$\}$。Caragiannis等人给出了二维四角网格图反馈数的上界, 本文改进了其上界。

Let $G = (V, E)$ be a simple graph and $F$ be a subset of $V$. If the subgraph induced by the subset $V-F$ does not contain cycles, then $F$ is called a feedback set of $G$. The smallest value of the numbers of vertices in feedback sets is called the feedback number of $G$, denoted by $f(G)$, that is, $f(G)=\min\{|F| : F$ is a feedback set of $G\}$. Caragiannis et al. obtained the upper bounds of the feedback number of 2-dimensional meshes. In this paper, we improve the upper bounds.