In the edge detection model based on neural network, most of models have lower detection efficiency, and the detection effect needs to be improved. Inspired by the characteristics of biological vision systems, a new edge detection method based on Gaussian Positive-Negative (GPN) radial basis neural network is proposed in this study. Firstly, we construct a new GPN radial-based neural network, which takes each pixel point preprocessed by Gaussian filtering in the image as the center point of the GPN radial-based neural network and inputs it into the neural network. Then, the partial characteristics of the convolutional neural network are used between each layer for processing, and the results are output after the expansion layer and the hidden layer are calculated. Finally, the edges are extracted by the contour tracking method according to the output result. In this study, the corresponding numerical experiments are carried out in two aspects:detection effect and efficiency. For the composite images and some intensity inhomogeneous images, compared with the pulse-coupled neural network model, the genetic neural network model and the convolutional neural network model, the proposed model is improved in efficiency and the edge connectivity is better. The experimental results show that the proposed edge detection method based on GPN radial basis neural network is a new and effective edge detection method, which is more efficient than the traditional neural network edge detection method, and the detection effect is also improved.