Aiming at the problem of real-time image edge extraction, a quantum LoG image edge detection algorithm based on classical Gauss-Laplacian operator (LoG operator) is designed. By simulating the quantumLoG algorithm with Matlab software on a classical computer, it is proved that the quantum LoG algorithm can quickly and effectively realize the recognition and extraction of image edges. In addition, the influence of two types of decoherence effects on the algorithm is also investigated. The calculation results show that compared with the existing corresponding quantum image edge detection algorithms, the quantum LoG algorithm has better anti-noise characteristics.