Given a building floorplan, humans can localize themselves by matching the observation of the environment with the floorplan using geometric, semantic, and topological clues. Inspired by this insight, this paper proposes a learning- based topometric robot localization method FloorplanNet, which implements a match between a metric robot map and the potentially inaccurate building floorplan in nonuniform scales and different shapes by semantic information. The method uses a novel Graph Neural Network to learn descriptors of nodes from topometric graphs generated from the input maps. We demonstrate that our method can match the 3D point cloud sub-map generated by the robot during the SLAM process with the 2D map. Furthermore, we apply our map-matching algorithm for real-world robot localization. We evaluate our method on several publicly available real-world datasets. Even though our network is solely trained using simulation data, our method demonstrates high robustness and effectiveness in real- world indoor environments and outperforms the existing SOTA map-matching algorithms. We further develop a simulator that automatically creates and annotates the required training data to train our neural networks. The method and simulator are released at: https://github.com/fengdelin/FloorplanNet.git