Hāpuku (Polyprion oxygeneios) is a promising candidate for aquaculture production in New Zealand. Methods for spawning, juvenile production, and growout to harvest entirely on land, where water quality, pathogens, environmental impacts, and genetic “pollution” can be tightly controlled, have been developed, and genetic improvement to optimise land-based production is the obvious next step. However, estimates of genetic parameters are required to design a rigorous, disciplined, and effective selective breeding program. By using existing data consisting of irregularly spaced repeated measurements of fork length and live body weight collected on wild-collected founders and two generations of captively reared progeny, we evaluated the species’ genetic potential for improvement in growth. We first tested a range of univariate random regression models to identify the best-fitting models for these data. Subsequently, using a bivariate model, we estimated variance components for growth trajectories of fork length and whole body weight. With one to six records available per fish, the best-fitting univariate models included only a fixed effect for contemporary groups and fixed and random genetic third-order Legendre polynomials. More complex models that included full-sib family and/or permanent environmental effects produced unacceptable constrained and/or non-positive-definite solutions. Both traits are moderately heritable at all stages of the growout phase (~0.4–0.5), and the genetic correlation patterns between daily breeding values estimated via the covariance function are different for length and weight. Genetic correlations for length between all pairs of age-specific breeding values are positive and strong (>0.7) and change gradually and smoothly with increasing temporal separation. For weight, these correlations deteriorate more rapidly with increasing time lags between measurements and become negative for some age pairings. We conclude that random regression analyses are a valuable tool for extracting genetic information from irregularly spaced repeated measurements of fish size, speculate that emerging technologies for high-throughput genotyping and phenotyping will add to the value of this approach in the near future, and reason that a breeding strategy that rigorously takes into account the potentially unfavourable genetic correlations between breeding values for weight at some ages will further adapt hāpuku to land-based systems and enhance the profitability commercial-scale production.