The tropical abalone Haliotis asinina is a wild-caught and cultured species throughout the Indo-Pacific as well as being an emerging model species for the study of haliotids. H. asinina has the fastest recorded natural growth rate of any abalone and reaches sexual maturity within one year. As such, it is a suitable abalone species for selective breeding for commercially important traits such as rapid growth. Estimating the amount of variation in size that is attributable to heritable genetic differences can assist the development of such a selective breeding program. Here we estimated heritability for growth-related traits at 12 months of age by creating a single cohort of 84 families in a full-factorial mating design consisting of 14 sires and 6 dams. Of 500 progeny sampled, 465 were successfully assigned to their parents based on shared alleles at 5 polymorphic microsatellite loci. Using an animal model, heritability estimates were 0.48 ± 0.15 for shell length, 0.38 ± 0.13 for shell width and 0.36 ± 0.13 for weight. Genetic correlations were > 0.98 between shell parameters and weight, indicating that breeding for weight gains could be successfully achieved by selecting for shell length.