Random regression (RR) analysis has been recommended to estimate the genetic parameters of longitudinal data. The objective of this study was to evaluate the growth of turkeys using RR models. Data were collected from 957 turkeys and included 15 478 individual body weight recorded during the first week of life and between weeks 2 and 32 by 2-week intervals. To take into account the repeated measurements of weight for each animal, a specific overall growth curve was modelled using a cubic smoothing spline. Animal deviation to this curve was also modelled using an RR function. All data were analysed with the ASReml package. The results showed an increase in heritability estimates over the trajectory and peaked at 0.60 around 20 to 32 weeks of age. Genetic correlations showed that turkeys could be selected at earlier time points, at 12 weeks of age, in order to increase the growth rate. In general, genetic correlation estimates were higher among adjacent ages, decreasing markedly with the increase of distance between ages. Negative genetic correlations were observed between ages.