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In this paper, we propose a semantic simultaneous localization and mapping (SLAM) framework for rescue robots, and report its use in navigation tasks. Our framework can generate not only geometric maps in the form of dense point-clouds but also corresponding point-wise semantic labels generated by a semantic segmentation convolutional neural network (CNN). The semantic segmentation CNN is trained using our RGB-D dataset of the RoboCup Rescue-Robot-League (RRL) competition environment. With the help of semantic information, the rescue robot can identify different types of terrains in a complex environment, so as to avoid specific obstacles or to choose routes with better traversability. To reduce the segmentation noise, our approach utilizes depth images to perform filtering on the segmentation results of each frame. The overall semantic map is then further improved in the point-cloud voxels. By accumulating results of multiple frames in the voxels, semantic maps with consistent semantic labels are obtained. To show the advantage of having a semantic map of the environment, we report a case study of how the semantic map can be utilized in a navigation task to reduce the arrival time while ensuring safety. The experimental result shows that our semantic SLAM framework is capable of generating a dense semantic map for the complex RRL competition environment, with which the arrival time of the navigation time is effectively reduced.