This study aimed to estimate genetic parameters, effective population size, inbreeding, and inbreeding depression for birth weight, weaning weight, and average pre-weaning daily weight gain (ADG) in Piau breed pigs. We used information from 3841 Piau pigs, and four linear models were fitted in single trait analyzes including or excluding maternal genetic effect, common litter effect, or a combination of these. The models’ adjustments were compared by likelihood ratio test, in which the model that presented the best fit for each trait was used to estimate (co)variance components. The inbreeding depression effect was evaluated using a linear model that included the fixed effects of sex, parity order, contemporary group, and inbreeding coefficient as a fixed covariate. Weight at birth and weaning showed low direct heritabilities (0.08 and 0.05, respectively), while ADG showed moderate heritability (0.20). Weight at birth showed high genetic correlations with weight at weaning (0.90) and with ADG (0.82). Weight at weaning and ADG also showed a high genetic correlation (0.99). There was an inbreeding increase over the generations and a reduction of the effective population size. In the last generation evaluated all animals were inbred, the average inbreeding coefficient was 0.07 and the effective population size was 20.8. It was observed a significant inbreeding effect on ADG, wherein an increase of 1% on the inbreeding coefficient resulted in a decrease of 0.005 grams on ADG. Thus, increase effective population size is mandatory for the inbreeding control and to reduce the loss of variability in this Piau population.