Spin-gapless semiconductors are considered as promising candidates for spintronic and magnetoelectronic materials. Enormous efforts have been devoted to search for materials in this regard. Recently, a new diamond-like quaternary semiconductor CuMn2InSe4 has been successfully synthesized by experiment and also demonstrated as spin-gapless semiconductor in theory. In this work, we report a theoretical study on the electronic, magnetic and thermodynamic properties of the CuMn2InSe4 under strain conditions by employing the first-principles calculations and quasi-harmonic Debye model. Under uniform strain, the spin-gapless semiconducting nature can only be maintained from 0% to 5% at the stretching side yet immediately destroyed at the compressing side. Although the magnetic moments of all atoms vary continuously with uniform strain, the total magnetic moment shows a good stability against uniform stretching up to 5%. The effect of the tetragonal distortion has also been studied in terms of strains in lattice a and c separately. Results show that strain in a has an important impact and induces larger variation on both the electronic and magnetic properties than in c. CuMn2InSe4 easily loses its spin-gapless semiconducting feature with the variation of strain in a but it can be maintained considerably better by strain in c. In particular, this spin-gapless behavior preserves through the whole studied range of strain in c from −5% to +5% at 100% a. While, the magnetic moments of all atoms under tetragonal distortion show the same variation tendencies under strain in a or c and the changing rate is a slightly larger with strain in a. Additionally, the thermodynamic properties of CuMn2InSe4 are predicted through the quasi-harmonic Debye model. The variation of bulk modulus, lattice constant, heat capacity, thermal expansion coefficient, Grüneisen constant and Debye temperature with pressure and temperature are successfully obtained. To the best of our knowledge, neither experimental nor theoretical reports regarding the electronic, magnetic and thermodynamic properties under strain conditions for CuMn2InSe4 compound are available in the literature and, thus, our results can give a helpful reference or even inspire new studies for this kind of material in the future work.