Resumo. ABSTRACT The objective of this article was to estimate the genetic variability and selection gain in the characters related with fruits in assai palms, 68 progenies collected in populations from Afuá city and planted in Amapá state were evaluated. The experiment was conducted in random blocks with two replications and four useful plants per plot. The following characters were evaluated: fruit longitudinal diameter (DLF), the fruit greatest transversal diameter (DTMA), the smallest fruit diameter (DTME); mass from one hundred fruits (P100) and, in bunches: total fruit mass (PTC). There are differences between progenies, denoting the possibility of selection gains. In general, the inheritabilities were medium or high for the characters, but always lower for PTC. The coefficient CVg/CVe was favorable in DTMA and DTME and unfavorable to PTC; the correlations between characters were positive and significant, the selection gain was 16.65% for PTC and from -1.29% to -7.60% in the other characters; the selected progenies were able to associate the desired values in the evaluated characters. The obtained conclusions were that there is high environmental contribution in the phenotypic manifestation of the progenies once the fruit metric dimensions had lower environmental effects and higher genetic effect; there is possibility of genetic gains which are important to breeding programs of this species using the characters simultaneously, although the values had been low, mainly due to the positive correlation presence, where there is preference for reduced fruit size with productivity increase.