Components of (co)variance and genetic parameters were estimated for adjusted weights at ages 120 (W120), 240 (W240), 365 (W365) and 450 (W450) days of Polled Nellore cattle raised on pasture and born between 1987 and 2010. Analyses were performed using an animal model, considering fixed effects: herd-year-season of birth and calf sex as contemporary groups and the age of cow as a covariate. Gibbs Samplers were used to estimate (co)variance components, genetic parameters and additive genetic effects, which accounted for great proportion of total variation in these traits. High direct heritability estimates for the growth traits were revealed and presented mean 0.43, 0.61, 0.72 and 0.67 for W120, W240, W365 and W450, respectively. Maternal heritabilities were 0.07 and 0.08 for W120 and W240, respectively. Direct additive genetic correlations between the weight at 120, 240, 365 and 450 days old were strong and positive. These estimates ranged from 0.68 to 0.98. Direct-maternal genetic correlations were negative for W120 and W240. The estimates ranged from -0.31 to -0.54. Estimates of maternal heritability ranged from 0.056 to 0.092 for W120 and from 0.064 to 0.096 for W240. This study showed that genetic progress is possible for the growth traits we studied, which is a novel and favorable indicator for an upcoming and promising Polled Zebu breed in Tropical regions. Maternal effects influenced the performance of weight at 120 and 240 days old. These effects should be taken into account in genetic analyses of growth traits by fitting them as a genetic or a permanent environmental effect, or even both. In general, due to a medium-high estimate of environmental (co)variance components, management and feeding conditions for Polled Nellore raised at pasture in tropical regions of Brazil needs improvement and growth performance can be enhanced.