In this paper, a novel LiDAR–inertial-based Simultaneous Localization and Mesh Reconstruction (LI-SLAMesh) system is proposed, which can achieve fast and robust pose tracking and online mesh reconstruction in an outdoor environment. The LI-SLAMesh system consists of two components, including LiDAR–inertial odometry and a Truncated Signed Distance Field (TSDF) free online reconstruction module. Firstly, to reduce the odometry drift errors we use scan-to-map matching, and inter-frame inertial information is used to generate prior relative pose estimation for later LiDAR-dominated optimization. Then, based on the motivation that the unevenly distributed residual terms tend to degrade the nonlinear optimizer, a novel residual density-driven Gauss–Newton method is proposed to obtain the optimal pose estimation. Secondly, to achieve fast and accurate 3D reconstruction, compared with TSDF-based mapping mechanism, a more compact map representation is proposed, which only maintains the occupied voxels and computes the vertices’ SDF values of each occupied voxels using an iterative Implicit Moving Least Squares (IMLS) algorithm. Then, marching cube is performed on the voxels and a dense mesh map is generated online. Extensive experiments are conducted on public datasets. The experimental results demonstrate that our method can achieve significant localization and online reconstruction performance improvements. The source code will be made public for the benefit of the robotic community.