Several newly designed Zinc-based all-d-metal Heusler alloys, Zn2MMn (M = Ru, Rh, Pd, Os, Ir), have been predicted, and their XA- and L21-type atomic-site preferences, electronic structures, magnetic properties, as well as their possible martensitic phase transformations have been studied theoretically from first principles. For cubic-type these alloys, their L21-type phase is more stable than the XA phase, that is, the two Zn atoms prefer to locate at the A (0,0,0) and C (0.5, 0.5, 0.5) positions in the lattice. Their magnetic state is ferromagnetic (FM), with a large total magnetic moment (> 3µB/f.u), and the total magnetic moment arises mainly from the Mn atom due to its strong exchange splitting. Remarkably, Zn2MMn alloys with a tetragonal martensitic structure can lower their total energies and show more stable behaviour than cubic systems. The energy difference ΔEMis defined as the difference in total energy between the martensitic and cubic states. Δ EMcan be tuned by uniform strain, namely, as the lattice constant increases, Δ EMalso increases. Moreover, in the case of martensitic-type Zn2RuMn and Zn2OsMn alloys, quite large c/a ratios (1.41, 1.43, respectively) can be found, which are preferable for the transformation strain effect. It is hoped that this work can motivate researchers to look for new spintronic and magnetic-intelligent materials among all-d-metal Heusler alloys.