Plant leaf image recognition is one of important applications of computer vision and image processing technology to biology and modern agriculture. It is a challenging problem due to the large size of the plant species community and great inter-class similarity, which makes it very difficult to describe the variants between classes of leaf images. In this study, a novel shape description method, Gaussian convolution angle, is proposed for identifying leaf image. For each contour point, its left and right neighborhood vectors are convolved with a Gaussian function respectively to form Gaussian convolution angle. By changing the scale parameter of the Gaussian function, multiscale Gaussian convolution angles are derived to form a feature vector. Combing the feature vectors of all the contour points, a set of feature vectors is built for describing leaf shape. The similarity of the two leaf images can be simply measured by calculating the Hausdorff distance between their feature vector sets. The proposed Gaussian convolution angle descriptor is inherently invariant to translation, rotation, scaling, and mirror transformation which have been theoretically proved in this study. The descriptor also has the excellent characteristics of describing the leaf shape from coarse to fine, which makes it have a strong ability to identify the leaf. Two publicly available leaf image datasets are used to test the performance of the proposed method. The experimental results show that the proposed method outperforms the state-of-the-art methods on leaf image recognition, which indicates the effectiveness of the proposed method.