Tropical forest biomass is a crucial component of global carbon emission estimations. However, calibration and validation of such estimates require accurate and effective methods to estimate in-situ above ground biomass (AGB). Present methods rely on allometric models that are highly uncertain for large tropical trees. Terrestrial laser scanning (TLS) tree modelling has demonstrated to be more accurate than these models to infer forest AGB. Nevertheless, applying TLS methods on tropical large trees is still challenging. We propose a method to estimate AGB of large tropical trees by 3D tree modelling of TLS point clouds. Twenty-nine plots were scanned with a TLS in three study sites (Peru, Indonesia and Guyana). We identified the largest tree per plot (mean DBH of 73.5 cm), extracted its point cloud and calculated its volume by 3D modelling its structure using quantitative structure models (QSM) and converted to AGB using species-specific wood density. We also estimated AGB using pantropical and local allometric models. To assess the accuracy of our and allometric methods, we harvest the trees and took destructive measurements. AGB estimates by the TLS-QSM method showed the best agreement in comparison to destructive harvest measurements (28.37% CV-RMSE and Concordance Correlation Coefficient (CCC) of 0.95), outperforming the pantropical allometric models tested (35.6 to 54.95% CV-RMSE and CCC of 0.89 to 0.73). TLS-QSM showed also the lowest bias (overall underestimation of 3.7%) and stability across tree size range, contrasting with the allometric models that showed a systematic bias (overall underestimation ranging 15.2 to 35.7%) increasing linearly with tree size. The TLS-QSM method also provided accurate tree wood volume estimates (CV RMSE of 23.7%) with no systematic bias regardless the tree structural characteristics. Our TLS-QSM method accounts for individual tree biophysical structure more effectively than allometric models, providing more accurate and less biased AGB estimates for large tropical trees, independently of their morphology. This non-destructive method can be further used for testing and calibrating new allometric models, reducing the current underrepresentation of large trees in, and enhancing present and past estimates of forest biomass and carbon emissions from tropical forests.