We introduce a simple and effective point descriptor, called 3D Laplacian Pyramid Signature (3DLPS), by extending and adapting the Laplacian Pyramid defined in 2D images to 3D shapes. The signature is represented as a high-dimensional feature vector recording the magnitudes of mean curvatures, which are captured through sequentially applying Laplacian of Gaussian (LOG) operators on each vertex of 3D shapes. We show that 3DLPS organizes the intrinsic geometry information concisely, while possessing high sensitivity and specificity. Compared with existing point signatures, 3DLPS is robust and easy to compute, yet captures enough information embedded in the shape. We describe how 3DLPS may potentially benefit the applications involved in shape analysis, and especially demonstrate how to incorporate it in point correspondence detection, best view selection and automatic mesh segmentation. Experiments across a collection of shapes have verified its effectiveness.