Non-invasive edge detection of leaves is the key step of leaf feature extraction. Traditional algorithms for edge detection of leaves are usually invasive, since the detection is carried out after the leaves are picked. We apply order morphology in this study to non-invasive edge detection of leaves. First we analyze the algorithm for order morphology edge detection of leaves. In particular, the impact of structural elements and percentile on the detection is discussed. Based on the theory of order morphology transform of leaf images, the operator for detecting the leaf edge is constructed. Finally simulation experiment is carried out on leaf images under the conditions of natural illumination and artificial noise, respectively. Results show that the proposed algorithm is accurate and fast in leaf edge extraction and not sensitive to noise.