The Mn-based Mn2MoAl type ternary Heusler alloy is of particular interest due to its potential ferromagnetic properties and high spin-polarization. The present paper aims to explore the physical properties of this new alloy for its possible technological applications and also provide theoretical basis to the future experiments. The electronic structure, magnetism, and elastic properties of the alloy are studied by using first-principles calculations based on density functional theory (DFT), along with calculation of thermodynamic properties within quasi-harmonic approximation. The structural analysis predicts the optimized lattice constant of 5.90 Å and the ferromagnetic stable state. The electronic band structure calculations at GGA-level reveal that present alloy is nearly half-metal with spin-polarization up to 94% at the Fermi level, whereas, GGA + U calculations reveal Mn2MoAl alloy to be a quite spin polarized metal. The calculated total magnetic moment Mt of the unit-cell is found to be 1.04 μB, which nearly obeys Mt = │Zt-24│formula. The individual Mn, Mo and Al atoms carry magnetic moment of 0.70 μB, -0.28 μB, -0.01μB, respectively. Employing quasi-harmonic approximation, interesting thermodynamic properties of the alloy have been investigated. Furthermore, the elastic and mechanical properties have been investigated. The results confirm that Mn2MoAl alloy is mechanically stable, ductile, anisotropic, with metallic inter-atomic bonding and is expected to be beneficial for the spintronic technology.