The objectives of the current study were to evaluate the genetic progress and variability for growth traits and also to suggest a suitable direction to the existing breeding program of the Barbari goat population in India. The analysis included 10,648 animals descended from 2697 dams and 420 sires at the ICAR-Central Institute for Research on Goats, Makhdoom between 1993 and 2020 (28 years). The effect of fixed factors such as period and season of kidding, sex of the kid, type of birth, parity of doe, and doe weight at kidding on live weights were significant (P < 0.05). Animal models with average information restricted maximum likelihood (AIREML) approach were used to estimate genetic parameters for growth traits. The mean of inbreeding coefficient for the whole pedigree was 2.16%. For the inbred animals it was 3.32%, indicating within normal estimate for average inbreeding in a nucleus flock. Results suggested that the genetic model for additive direct effects of animal and dam and their covariance, as well as dam's permanent environment, was best for birth weight (BW), weaning weight (WW), weight at six months (6 W), and weight at nine months (9 W), whereas the model with direct effects of animal and dam and their covariance was best for weight at 12 months (12 W). The estimates of direct heritability (h2) for Barbari goat were 0.31 ± 0.04, 0.23 ± 0.03, 0.18 ± 0.03, 0.13 ± 0.03 and 0.21 ± 0.04 for BW, WW, 6 W, 9 W, and 12 W, respectively. However, the estimates were influenced by negative correlation between direct additive effects of animal and dam. We also observed substantial variance for additive maternal effect (0.09–0.15) and maternal permanent environment effect (0.11–0.17) across traits analysed. Pre-weaning growth traits had a significant maternal effect that receded as age advanced. The prospect of selecting Barbari goats for growth traits is indicated by moderate h2 estimates. The positive and desired genetic trend revealed favourable response to selection in the nucleus of the Barbari goat for growth traits. The significant and positive genetic and phenotypic correlation between post-weaning weights (6–9 W= 0.89) suggests scope for early selection of Barbari goats by decreasing the age for selection from 9 to 6 months.