Precise quantification of 3D forest structure will contribute to improve knowledge on ecosystem functioning and is required for sustainable forest management. However measuring forest structure from traditional field measurements is tedious. We propose an innovative method to quantify 3D spatial distribution of forest vegetation from terrestrial lidar data. The method rests on the hypothesis that the ratio of laser beams intercepted within a given volume element (voxel) is proportional to the vegetation density inside this voxel. Consequently a density index was computed for each voxel of the plot space as the ratio between the number of returns inside the voxel and the number of laser beams entering it. To make computation easier, analysis were conducted in a spherical coordinate system in accordance with acquisition geometry. The model was applied to individual trees and forest plots using various scan densities and distances. Resulting density index represents well the vegetation structure as visually observed within the lidar point cloud and normalizes lidar information. However, to ensure reliability of index values, it was necessary to reject voxels with high occlusion levels (over 60% of laser beams intercepted before reaching the voxel). The density indices were then aggregated at the tree level to be related to tree measurements or used to compute vegetation profiles at the plot level reflecting plot characteristics collected in the field. Despite an anisotropy of the index values due to tree architecture, results show that the proposed method is effective to derive from terrestrial lidar data meaningful dataset expressing 3D forest structure and in connection with dendrometric characteristics at both plot and tree levels;