The crystal structure, electronic and magnetic properties of the new full-Heusler compounds Zr 2 MnZ (Z=Al, Ga, In), were studied within the Density Functional Theory (DFT) framework. The materials exhibit unique properties that connect the spin gapless semiconducting character with the completely compensated ferrimagnetism. In magnetic configurations, Zr 2 MnZ (Z=Al, Ga, In) crystallize in inverse Heusler structure, are stable against decomposition and have zero magnetic moment per formula unit properties, in agreement with Slater-Pauling rule. The Zr 2 MnAl compound presents spin gapless semiconducting properties with a energy band gap of 0.41 eV in the majority spin channel and a zero band gap in the minority spin channel. By substituting Ga or In elements, for Al in Zr 2 MnAl, semiconducting pseudo band gaps are formed in the majority spin channels due to the different neighborhood around the manganese atoms, which decreases the energy of Mn's triple degenerated anti-bonding states.