First-order phase transitions are accompanied by a latent heat. Consequently, manipulating them by means of an external field causes a caloric effect. Although transitions from antiferromagnetic to paramagnetic states are not controlled by a magnetic field, a large barocaloric effect is expected when strong cross-correlations between the volume and magnetic order occur. Here we examine how geometric frustration in itinerant antiferromagnetic compounds can enhance the barocaloric effect. We study the thermodynamic behaviour of the frustrated antiferromagnet Mn3GaN, and report an entropy change of 22.3 J kg(-1) K-1 that is concomitant with a hydrostatic pressure change of 139 MPa. Furthermore, the calculated value of the adiabatic temperature change reaches 5 K by depressurization of 93 MPa. The giant barocaloric effect in Mn3GaN is caused by a frustration-driven enhancement of the ratio of volume change against the pressure coefficient of the Neel temperature. This mechanism for enhancing the barocaloric effect can form the basis for a new class of materials for solid-state refrigerants.