The link between species’ functional traits and competitive abilities has been described as a major factor structuring plant communities. However, two diverging hypotheses have been proposed to explain this process: competition-trait similarity and competition-trait hierarchy. We performed a greenhouse experiment to determine whether grasses’ root foraging strategies, from acquisitive or conservative functional groups, are linked to plant competitive ability and to test which hypothesis better explains interactions during the early stage of grass establishment under contrasting growth conditions. Two grass species of each functional group were grown with and without a neighbour under two levels of water and phosphorus supplies. Three functional traits related to plant competitive ability were measured on all plants grown without neighbours: specific root length (SRL), root phosphorus use efficiency and root length density. Above-ground biomass was measured on plants grown with and without neighbours to evaluate the intensity of plant interaction. We demonstrated that for the three traits the intensity of interaction is driven mainly by hierarchical trait distance, that is, trait distance between target and neighbour, and not by trait similarity. Growth conditions strongly affected the significance of the relation between hierarchical distances and competition intensity. For the SRL hierarchical distance, this effect may be due to the most competitive species (with high SRL) being strongly impacted by water shortage, which modified the competitive hierarchy. Trait plasticity in response to stresses also appeared an important factor influencing the competitive ability of species, that is, species with the most plastic SRL in response to P stress were also the most competitive under P stress. A strong hierarchy exists among grasses’ competitive abilities in non-limiting growth conditions that is linked to their root functional traits and investment in the root system. Consequently, our results support the trait hierarchy hypothesis in its ability to describe competitive interaction among grasses during early stages of establishment. Our study provides evidence that root functional hierarchical trait distance and plasticity explain how grasses interact with their neighbours. This distance enables species to be ranked according to their competitive ability; however, this ranking may be influenced by the growth conditions and traits considered.