The strength and persistence of the tropical carbon sink hinges on the long‐term responses of woody growth to climatic variations and increasing CO2. However, the sensitivity of tropical woody growth to these environmental changes is poorly understood, leading to large uncertainties in growth predictions. Here, we used tree ring records from a Southeast Asian tropical forest to constrain ED2.2‐hydro, a terrestrial biosphere model with explicit vegetation demography. Specifically, we assessed individual‐level woody growth responses to historical climate variability and increases in atmospheric CO2 (Ca). When forced with historical Ca, ED2.2‐hydro reproduced the magnitude of increases in intercellular CO2 concentration (a major determinant of photosynthesis) estimated from tree ring carbon isotope records. In contrast, simulated growth trends were considerably larger than those obtained from tree rings, suggesting that woody biomass production efficiency (WBPE = woody biomass production:gross primary productivity) was overestimated by the model. The estimated WBPE decline under increasing Ca based on model‐data discrepancy was comparable to or stronger than (depending on tree species and size) the observed WBPE changes from a multi‐year mature‐forest CO2 fertilization experiment. In addition, we found that ED2.2‐hydro generally overestimated climatic sensitivity of woody growth, especially for late‐successional plant functional types. The model‐data discrepancy in growth sensitivity to climate was likely caused by underestimating WBPE in hot and dry years due to commonly used model assumptions on carbon use efficiency and allocation. To our knowledge, this is the first study to constrain model predictions of individual tree‐level growth sensitivity to Ca and climate against tropical tree‐ring data. Our results suggest that improving model processes related to WBPE is crucial to obtain better predictions of tropical forest responses to droughts and increasing Ca. More accurate parameterization of WBPE will likely reduce the stimulation of woody growth by Ca rise predicted by biosphere models. The sensitivity of tropical woody growth, which fundamentally drives tropical carbon sink, to climatic variations and increasing CO2 is poorly understood. We used tropical tree ring records to constrain a terrestrial biosphere model. We found that model‐data discrepancy in tree growth is most likely caused by a lack of woody biomass production efficiency (WBPE) responses to CO2 and hydroclimate. More accurate parameterization of WBPE will likely reduce the stimulation of woody growth by CO2 rise and increase growth resilience to dry periods predicted by biosphere models.