We investigated the effects of family selection on the growth rates of four genetic lines of Litopenaeus vannamei, the Pacific white shrimp, from Venezuela. The mean family weight at selection was 16.79 g and the mean growth rate was 0.169 g d-1 at a mean age of 138 days. The mean growth rates per generation were 0.141 g d-1 for the parental generation (P0), 0.173 g d-1 for the F1 and 0.191 g d-1 for the F2. Survival varied from 83.3% to 94.4%. There were statistically significant differences between lines, with lines B and C, growing at higher temperatures and lower salinities, showing the fastest growth. Regression analysis between growth rate and age for each genetic line showed high r² values, but smaller than those shown between growth rate and generation. The mean heritability (h²) estimated for growth rate was 0.25 ± 0.04, with line per generation values ranging from 0.18 to 0.38. The mean heritability for growth rate per line showed some variation but there was no correlation between heritability and growth rate. Females showed a greater gain in growth rate per generation than males due to their faster growth when they were older. This study shows the high potential of these L. vannamei populations for the future of shrimp culture in the Americas.