Existing methods for recognizing polygons can be improved. A new concept “homograph” and then a new method for recognizing polygons based on the principle of homograph are proposed. First six topological characteristics and geometrical characteristics are introduced that are invariant to describe polygon under affine transformation. Then, the new concept of homograph is defined in terms of six topological characteristics and geometrical characteristics. Based on of this definition, a new algorithm is proposed for recognizing that two polygons are homograph. The topological structure is introduced to analyze homograph qualitatively, the algorithm is insensitive to noises; and the geometrical structure is introduced to analyze homograph quantitatively, thus the algorithms can show tiny differences between polygons. It can not only recognize objects with different shape but also distinguish between objects with the same shape but with different sizes and scales. Comparing with other recognition algorithms, the algorithm presented showed apparent improvement. The effectiveness of the algorithm is demonstrated by experiments.