Tree-level information can be estimated based on light detection and ranging (LiDAR) point clouds. We propose to develop a quantitative structural model based on terrestrial laser scanning (TLS) point clouds to automatically and accurately estimate tree attributes and to detect real trees for the first time. This model is suitable for forest research where branches are involved in the calculation. First, the Adtree method was used to approximate the geometry of the tree stem and branches by fitting a series of cylinders. Trees were represented as a broad set of cylinders. Then, the end of the stem or all branches were closed. The tree model changed from a cylinder to a closed convex hull polyhedron, which was to reconstruct a 3D model of the tree. Finally, to extract effective tree attributes from the reconstructed 3D model, a convex hull polyhedron calculation method based on the tree model was defined. This calculation method can be used to extract wood (including tree stem and branches) volume, diameter at breast height (DBH) and tree height. To verify the accuracy of tree attributes extracted from the model, the tree models of 153 Chinese scholartrees from TLS data were reconstructed and the tree volume, DBH and tree height were extracted from the model. The experimental results show that the DBH and tree height extracted based on this model are in better consistency with the reference value based on field survey data. The bias, RMSE and R² of DBH were 0.38 cm, 1.28 cm and 0.92, respectively. The bias, RMSE and R² of tree height were-0.76 m, 1.21 m and 0.93, respectively. The tree volume extracted from the model is in better consistency with the reference value. The bias, root mean square error (RMSE) and determination coefficient (R²) of tree volume were-0.01236 m³, 0.03498 m³ and 0.96, respectively. This study provides a new model for nondestructive estimation of tree volume, above-ground biomass (AGB) or carbon stock based on LiDAR data.