The growth of Nelore cattle was analysed considering the following performance parameters; the effect of the calving order of cows on the phenotypic expression of birth weight (BW), average daily gain from birth to weaning (BWG), and weaning weight (WW), the estimated genetic parameters for the traits, including the covariance components between direct and maternal genetic effects. Genetic trends and correlated responses were also obtained for the studied traits. The calving order of cows, as well as other fixed effects used to obtain the adjusted phenotypic means, were statistically significant (p < 0.001) for studied traits. Direct heritability was estimated at 0.24 ± 0.01 (BW), 0.15 ± 0.01 (BWG), and 0.18 ± 0.01 (WW), while maternal heritability was 0.06 ± 0.01 (BW), 0.12 ± 0.01 (BWG), and 0.11 ± 0.01 (WW). The correlations between direct and maternal effects within the same trait were negligible. Moderate to higher direct genetic correlations (ranging from 0.54 ± 0.04 to 0.98 ± 0.01) and maternal genetic correlations (ranging from 0.34 ± 0.09 to 0.99 ± 0.002) were estimated between the studied traits. Unlike direct genetic effects, there was no significant change in maternal genetic effects over time (p > 0.05). These results indicated the need for revising selection indexes for enhancing maternal ability. Correlated responses were generally lower compared to direct responses, except for BWG. The selection for BWG, considering the maternal genetic effect, would be more efficient to improve maternal ability of the cows for pre-weaning growth in relation to selection for WW. Our results found that direct genetic merit improves pre-weaning weight and this trait can be incorporated into the breeding goal as reflected in the WW.