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Although the tambaqui (Colossoma macropomum) is the most cultivated native fish species in Brazil, estimated breeding values for growth traits are rarely used for selection of superior individuals in commercial fingerling production. This study aimed to estimate the (co)variance components of growth traits. Body weight, length and width of 2500 tambaqui were determined at tagging and at 6 and 12 months after tagging in a commercial breeding programme in Brazil. Heritability estimates were low for traits measured at tagging (0.10 to 0.19) and moderate to high for traits measured at 6 and 12 months (0.23 to 0.81). Common full-sib effects were high at tagging (>73%), low at 6 months and negligible at 12 months. Positive genetic correlations were found among growth traits at 12 months (0.84 to 0.99) and between growth traits at 6 and 12 months (0.80 to 0.92). These results show that animal selection can be performed at 6 months after tagging. Expected genetic gains for growth traits ranged from 8% to 31%. A simulation of the sex ratio was performed, as individuals did not reach sexual maturity during the experimental period. Because of the sexual dimorphism, more accurate heritability estimates were obtained when considering the female proportion to be 90% in the high-weight group. The findings indicate that it is possible to obtain considerable genetic gains in growth by selecting for growth traits. The development of a tool to determine the sex of animals at early stages can improve the response to selection in tambaqui.