Employing first-principle calculations, we have investigated electronic and magnetic properties of the Zr-based quaternary Heusler alloys: ZrCoVIn, ZrFeVGe, ZrCoFeP, ZrCoCrBe and ZrFeCrZ (Z = In and Ga). Our calculation results show that all the alloys are (or nearly) spin-gapless semiconductors. The Slater–Pauling behaviours of these alloys are discussed 30 as well. The cohesion energy and formation energy of these alloys have also been discussed, and the results indicate the studied alloys are stable.