Heusler compounds arewidely studied due to their variety of magnetic properties making them ideal candidates for spintronic and magnetoelectronic applications. V3Al in its metastable D0(3)-type Heusler structure is a prototype for a rare antiferromagnetic gapless behavior. We provide an extensive study on the electronic and magnetic properties of V3Al, V3Ga, and V3In compounds based on electronic structure calculations. We show that the ground state for all three is a G-type itinerant antiferromagnetic gapless semiconductor. The large antiferromagnetic exchange interactions lead to very high Neel temperatures, which are predicted to be around 1000 K. The coexistence of the gapless and antiferromagnetic behaviors in these compounds can be explained considering the simultaneous presence of three V atoms at the unit cell using arguments which have been employed for usual inverse Heusler compounds. We expect our study on these compounds to enhance further the interest on them towards the optimization of their growth conditions and their eventual incorporation in devices.