1. Plant functional traits, in particular specific leaf area (SLA), wood density and seed mass, are often good predictors of individual tree growth rates within communities. Individuals and species with high SLA, low wood density and small seeds tend to have faster growth rates. 2. If community-level relationships between traits and growth have general predictive value, then similar relationships should also be observed in analyses that integrate across taxa, biogeographic regions and environments. Such global consistency would imply that traits could serve as valuable proxies for the complex suite of factors that determine growth rate, and, therefore, could underpin a new generation of robust dynamic vegetation models. Alternatively, growth rates may depend more strongly on the local environment or growth–trait relationships may vary along environmental gradients. 3. We tested these alternative hypotheses using data on 27 352 juvenile trees, representing 278 species from 27 sites on all forested continents, and extensive functional trait data, 38% of which were obtained at the same sites at which growth was assessed. Data on potential evapotranspiration (PET), which summarizes the joint ecological effects of temperature and precipitation, were obtained from a global data base. 4. We estimated size-standardized relative height growth rates (SGR) for all species, then related them to functional traits and PET using mixed-effect models for the fastest growing species and for all species together. 5. Both the mean and 95th percentile SGR were more strongly associated with functional traits than with PET. PET was unrelated to SGR at the global scale. SGR increased with increasing SLA and decreased with increasing wood density and seed mass, but these traits explained only 3.1% of the variation in SGR. SGR–trait relationships were consistently weak across families and biogeographic zones, and over a range of tree statures. Thus, the most widely studied functional traits in plant ecology were poor predictors of tree growth over large scales. 6. Synthesis. We conclude that these functional traits alone may be unsuitable for predicting growth of trees over broad scales. Determining the functional traits that predict vital rates under specific environmental conditions may generate more insight than a monolithic global relationship can offer.