Fully compensated ferrimagnetic spin-gapless semiconductors (FCF-SGSs) have been recently proposed as a new class of materials for potential applications in spintronic devices. In this work, based on first-principles calculations, we have designed a new half-metallic fully compensated ferrimagnet (HM-FCF), Zr2MnAl, with a total magnetic moment that satisfies the Mt = Zt − 18 rule (where Mt is the total magnetic moment per unit cell and Zt is the total number of valence electrons). Importantly, uniform strains can drive Zr2MnAl to display diverse electronic and magnetic properties, from nonmagnetic semiconductor (NM) → fully compensated ferrimagnetic semiconductor (FCFS) → HM-FCF → FCF-SGS → FCFS → FCF-SGS → HM-FCF → metallic ferrimagnet (MFi) transitions, indicating high tunability of its electrons and magnetism near the Fermi surface. Our results show that Zr2MnAl not only is a potential candidate spin filter, but also can cater for various applications in spintronics devices subjected to strain tuning. Finally, the structural stability of Zr2MnAl and a possible rule to design FCF-SGSs are also discussed in detail.