In the traditional edge detection models, due to the influence of artifact, occlusion and other factors, the detection efficiency is poor and the error is large, which affects the subsequent image processing. Therefore, this paper proposes a new edge detection method based on Gaussian positive-negative radial basis neural network (GPN-RBNN). Firstly, a novel GPNRBNN is constructed in this paper. Each pixel preprocessed by Gaussian filter in the image is taken as the central point of the GPNRBNN and input into the neural network. Then, the weight sharing and sparse connection in the convolutional neural network are used for processing the pixels. The results are output after the calculation in the extended layer and the hidden layer. Thirdly, the edge is extracted by contour tracking according to the output results. Finally, experiments are conducted on the composite image, part of the uneven gray image and medical images etc. Compared with other models, the efficiency of the proposed model is improved, and the edge connectivity is better.