Branch architecture provides crucial information for the understanding of plant trait variability and the adaptive strategies employed by trees in response to their environment. High-fidelity terrestrial laser scanning (TLS) data provide an accurate, efficient, and non-destructive means for constructing three-dimensional (3D) tree models and estimating architectural traits. However, the complex canopy structure of trees in natural forests and the presence of occlusion in TLS data pose significant challenges to achieving this goal. In this study, we present a novel algorithm, L₁-Tree, for the construction of 3D tree models and the estimation of architectural traits from TLS data. This algorithm is grounded in the L₁-Median algorithm and integrates a tree skeleton optimization procedure that considers the structural characteristics of tree branches. By comparing modeling results and manually derived branch traits for 24 trees of 24 species, we found that the L₁-Tree algorithm achieved precision, recall, and F-score values of 0.94 for branch identification, coefficient of determination, root-mean-squared error, and normalized root-mean-squared error of 0.998, 0.068 m, and 0.3 % for branch length estimation, and a respective value of 0.958, 0.257 cm and 0.9 % for branch radius estimation. Additionally, the branch identification accuracy and accuracy in branch architectural trait estimation remained satisfactory across branch orders. Compared to established 3D tree model construction algorithms (e.g., TreeQSM), our L₁-Tree algorithm demonstrated a superior capability in handling noisy environments and data gaps, making it a robust tool for TLS data-based tree architecture studies. Leaf-wood separation emerged as a crucial step influencing the performance of the L₁-Tree algorithm. We observed significant drop in branch identification accuracy when using an automatic leaf-wood separation algorithm as input, highlighting the urgent need to develop effective leaf-wood separation algorithms to generate high-quality wood point clouds for tree architecture studies.