The genetic parameters for growth and multiple-stress resistance in Litopenaeus vannamei at 7 and 15 weeks of age were estimated using sixty full-sib families (including 29 half-sib families) in the present study. The heritability of growth traits was estimated to be medium to high (0.256 ± 0.119 to 0.441 ± 0.124), and that of multiple-stress [simultaneous stress of high salt (35), low pH (6 ± 0.1) and high ammonia nitrogen (56 mg/L)] tolerance traits was low (0.029 ± 0.034 to 0.053 ± 0.058), suggesting the feasibility of selecting increasing growth traits and that genetic improvement of stress tolerance traits requires multi-generation breeding by family and intra-family selection. The genetic correlations of growth traits (body weight, total length, body length, carapace length, carapace width and abdominal length) at identical ages were high (0.855 ± 0.031 to 0.999 ± 0.0002) (P < 0.01). The highly significant correlations between growth traits showed that any growth trait could be replaced by other growth traits for indirect selection. The genetic correlations between growth traits and multiple-stress tolerance traits at identical ages were low, but the positive correlation (0.081 ± 0.129 to0.224 ± 0.125) indicated that selection of growth traits will have a positive correlation response to multiple-stress tolerance traits. There was a weak genetic positive correlation (0.285–0.342) (P < 0.05) in the growth traits between the two different age stages, however the genetic correlation in the multiple-stress tolerance traits between the two different age stages were low and not significant (P > 0.05).This suggests that selection for growth traits in L. vannamei at an early age may not be optimal and should be undertaken at later stages of growth.