The co-registration between SAR and optical images is a challenging task because of the speckle noise of SAR and the nonlinear radiation distortions (NRD), particularly in the one-look situation. In this paper, we propose a novel density descriptor based on the histogram of oriented primary edge structure (HOPES) for the co-registration of SAR and optical images, aiming to describe the shape structure of patches more firm. In order to extract the primary edge structure, we develop the novel multi-scale sigmoid Gabor (MSG) detector and a primary edge fusion algorithm. Based on the HOPES, we propose the co-registration method. To obtain stable and uniform keypoints, the non-maximum suppressed SAR-Harris (NMS-SAR-Harris) and deviding grids methods are used. NMS-SSD fast template matching and fast sample consensus (FSC) algorithm are used to further complete and optimize matching. We use two one-look simulated SAR images to demonstrate that the signal-to-noise ratio (SNR) of MSG is more than 10 dB higher than other state-of-the-stage detectors; the binary edge maps and F-score show that MSG has more accurate positioning performance. Compared with the other state-of-the-stage co-registration methods, the image co-registration results obtained on seven pairs of test images show that, the correct match rate (CMR) and the root mean squared error (RMSE) improve by more than 25% and 15% on average, respectively. It is experimentally demonstrated that the HOPES is robust against speckle noise and NRD, which can effectively improve the matching success rate and accuracy.