In this paper, we present an efficient geometric deep learning framework for estimating the spectrum of the Laplace-Beltrami (LB) operator, which captures the intrinsic properties of objects in geometric deep learning. The conventional finite element method (FEM) has a computational complexity of O(Nk), which is inefficient for processing large-scale mesh data. In this study, we utilize rich mesh features such as Gaussian curvature, mean curvature, and principal curvature using graph neural networks (GNNs) to estimate the LB spectrum. Experimental results show that the proposed method is about 5 times faster than FEM and provides competitive accuracy. In addition, we also release a large-scale real mechanical CAD model dataset built on the ABC dataset used for training and testing for reproducibility.