Two-dimensional structure-histogram based on skeleton is proposed for shape descriptor and shape recognition. The descriptor utilizes the shape skeleton information to achieve invariance of starting point, rotation, translation and scale of shape contour. The shape descriptor calculates the geodesic path distance ratio based on skeleton center and maximal disk radius ratio for each pair of skeleton points. The two structural features are combined to construct a new two-dimensional histogram matrix statistically for describing shape. The experimental results show that this shape descriptor not only has the characteristic of rigid invariance, but also achieves higher efficiency and retrieval precision in non-rigid situation.