In 2019–2020, trials were carried out with the aim of evaluating the possibilities of using an organic fertilizer, reported to have a biostimulant action, for promoting the growth of young olive trees. The experiments were implemented using both potted and field-grown trees. The effects of the organic fertilizer were evaluated with respect to trees treated with a chemical fertilizer; for potted trees a control without any fertilization was also used. Therefore, the compared treatments were: organic fertilization vs. chemical fertilization or no fertilization in the experiment with potted trees; organic fertilization vs. chemical fertilization in the experiment with field-grown trees. Non-fertilized potted trees had the lowest growth. The organic fertilizer, with respect to the chemical one, determined higher growth in both potted and field-grown trees (+22–29% of the increment of the trunk cross sectional area). In potted trees, it determined a rapid elongation of the stem (+30% of the increment of tree height with respect to chemically fertilized trees) and this likely favored the development of a higher number of leaves, which, together with an increase in their photosynthetic activity (in August, +27% with respect to chemical fertilized trees), created conditions for higher assimilate production and in turn greater tree growth. Trees in the field showed that the greater growth was not obtained at the expenses of reproductive growth, which increased to the same degree as the vegetative growth. Overall, the results support the biostimulant action of the organic fertilizer and indicate the possibility of its use to improve the growth of young olive trees.