Lateralisation (i.e. different functional and/or structural specialisations of the left and right sides of the brain) of aggression has been examined in several vertebrate species, while evidence for invertebrates is scarce. In this study, we investigated lateralisation of aggressive displays (boxing with forelegs and wing strikes) in the Mediterranean fruit fly, Ceratitis capitata. We attempted to answer the following questions: (1) do medflies show lateralisation of aggressive displays at the population-level; (2) are there sex differences in lateralisation of aggressive displays; and (3) does lateralisation of aggression enhance fighting success? Results showed left-biased population-level lateralisation of aggressive displays, with no consistent differences among sexes. In both male-male and female-female conflicts, aggressive behaviours performed with left body parts led to greater fighting success than those performed with right body parts. As we found left-biased preferential use of body parts for both wing strikes and boxing, we predicted that the left foreleg/wing is quicker in exploring/striking than the right one. We characterised wing strike and boxing using high-speed videos, calculating mean velocity of aggressive displays. For both sexes, aggressive displays that led to success were faster than unsuccessful ones. However, left wing/legs were not faster than right ones while performing aggressive acts. Further research is needed on proximate causes allowing enhanced fighting success of lateralised aggressive behaviour. This is the first report supporting the adaptive role of lateralisation of aggressive displays in insects.