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The paper put forward a new method of image edge detection based on grey entropy which was the first time to be applied into the field of image edge extraction. We let the median value of pixels in the neighborhood of the window be the reference sequence, and selected certain pixels from sixteen different directions as the comparative sequences according to the information of the image texture and pixel distribution. After carrying out the grey relational analysis, we employed the grey relational coefficients obtained to calculate the grey entropy. If the difference between the maximum grey entropy value and the minimum one is greater than a given threshold, we can determine the central pixel is an edge point, or it is a non-edge one. Experiments show that this method can achieve a better effect than other conventional algorithms, and it provides us a new approach to image edge detection.