ABSTRACT Acrocomia aculeata (Jacq.) Lodd. ex. Mart. (Arecaceae) is a neotropical oil palm of widespread occurrence in the American continent and with great economic potential for the energy and food sectors. Genetic breeding studies for the species are very recent, with a need for basic knowledge from the genetic diversity in agronomic traits. Thus, the aim of this work was to estimate genetic variance, heritability, and genetic gain as well as to propose strategies of selection. Two-year evaluations of eight agromorphological characteristics were carried out in two experimental fields composed of 50 open-pollinated progenies. The results revealed moderate heritability for progeny average to thorn density in the abaxial side ( = 0.402 in Pindorama) and relative chlorophyll index ( = 0.458 in Presidente Prudente). The selective accuracy was 0.634 and 0.677 for the same traits, respectively. In the combined analysis, the higher values of heritability were obtained to thorn density on the abaxial region of leaves and relative chlorophyll index (0.616 and 0.666, respectively). Moderate to high magnitude values of genetic gain was reached for traits with greatest agronomic interest, as plant height Gs (%) = 19.64, number of leaves Gs (%) = 26.43, stipe diameter at breast height Gs (%) = 12.51, and relative chlorophyll index Gs (%) = 38.12. In conclusion, the results indicate considerable genetic variability for the evaluated traits and suggest that their most effective use for the purpose of genetic gains would be based on the combined selection between and within progenies.