In order to improve the convergence rate of genetic algorithms based on edge detection, a novel edge detection method based on a good point set genetic algorithm (GGA) was proposed. The proposed method designed the crossover operation with the theory of good point set in which the progeny inherits the common genes of the parents which represent its family so as to improve the convergence rate of the genetic algorithm. Furthermore, before the algorithm was used for edge detection, the feature space of the image grey level was transformed into the feature space of the fuzzy entropy. Dissimilarity enhancement processing next was applied to the image by using a fuzzy entropy theory to filter the nonedge pixels so as to reduce the scale of the solution domain. This approach offered another efficient way to improve the convergence rate. Experimental results show the proposed algorithm performs very well in terms of convergence rate. The detected edge image is well localized, thin, and robustly resistant to noise.