In this paper, three edge detection algorithms based on LOG operator, Canny operator and wavelet transform were introduced briefly. Then, three edge detection algorithms were simulated and analysed by MATLAB. The subjects of analysis were three kinds of pictures, vehicles, ships and animals, and each group had three pieces. The results showed that the image edge obtained by the algorithm based on LOG operator had general outline but insufficient details, the image edge contour and details obtained by the Canny operator algorithm were relatively complementary, and the image edge obtained by the wavelet transform algorithm had more abundant contour and details. In terms of performance, the algorithm based on wavelet transform had the highest peak signal-to-noise ratio (PSNR), followed by the algorithm based on Canny operator and the algorithm based on LOG operator; in terms of detection time, the algorithm based on LOG operation was the longest, followed by the algorithm based on Canny operator and the algorithm based on wavelet transform.