Gradient-based edge detection is a straightforward method to identify the edge points in the original grey-level image. It is intuitive that in the human vision system the edge points always appear where the grey-level value is greatly changed. Spiral Architecture is a relatively new image data structure that is inspired from anatomical considerations of the primate's vision. In Spiral Architecture, each image is represented as a collection of hexagonal pixels. Edge detection on Spiral Architecture has features of fast computation and accurate localization. In this paper, we present and compare gradient-based edge detection algorithms on Spiral Architecture. The experimental results show that the edge detection on Spiral Architecture outperforms that on traditional square image structure.