This study aimed to estimate heritobilities of growth curve parameters of laying, hens, adjusted by von Bertalanffy function: genetic and phenotypic correlation between growth curve parameters and genetic and phenotypic correlation between parameters and productive reproductive traits. The heritabilities (h(2)) estimated based in a mixed model, composed hy the random effect of sire, dam within sire, and fixed effect of hatching, of asymptotic weight (A), maturing index (k) and age at the inflection point (t*) were .52+/-.18, .25+/-.12 and .25+/-.12, respectively. Therefore, the use of A parameter will result in major genetic improvement. The heritabilities of k and t* parameter showed non-additive genetic effects and/or maternal effects. Heritabilities showed sex-linkage effects to asymptotic weight. The genetic correlations between A and k and A anti t* were -.20+/-.29 and .21+/-.28, respectively. Therefore, if selection aims to increase asymptotic weight, there will be a reduction on maturity index and increase on age at the point of inflection. A and k genetic correlation estimates may used in selection programs to obtain different growth patterns. A high and negative phenotypic correlation was found between k and t*, suggesting that both traits express the earliness of growth. The paint of inflection estimated by von Bertalanffy function was not an acceptable index of age at sexual maturity. Sexual maturity, egg weight, hen-day egg production, egg mass and indirect feed efficiency were evaluated. These results indicate that the genetic correlation estimated between A and k and production traits showed that selection programs may be developed based on these parameters. The asymptotic weight showed acceptable genetic correlation with sexual maturity egg weight, egg production rate and egg mass, but it was not adequate to indirect feed efficiency. if selection aims to increase asymptotic weight, there will be an earlier and more productive strain, but with tower efficiency. Therefore, a study on the selection index that controls the undesirable correlated response is suggested.