Edge detection is the fundamental step of object identification in image processing. The present paper has introduced a new algorithm for detection of edges of gray images via polynomial evaluation based Gabor filtering (PEBGF). Proposed algorithm is applied to fit histograms for defining the index of each pixel according to their intensity values. In PEBGF, higher degree of polynomial coefficients are employed on input image to get the index of every pixels according to the intensity. Polynomial evaluation helps to decompose the high and low indexing values depending on the applied threshold, which helps to detect the fine edges. The results of the proposed method are more accurate while comparing it with other methods of edge detection techniques.