In the present study, the physical properties of the ground state in bulk and Co2CrAl Heuslerene compound are investigated by density functional theory (DFT). The effects of exchange-correlation potential on the calculations have been also investigated by GGA, GGA+U, and GGA+U+mBJ approximately. Here, three graphene-like structures with the thickness of about 8 Bohr have been labeled as α, β, and ϒ phases. The results demonstrate the mechanical stability of bulk Co2CrAl since it passes the elastic stability test. Having proved the static stability of the bulk and three Heuslerene shapes of Co2CrAl, it is essential to study dynamic stability as well. The accessible region in the thermodynamic phase diagrams confirms the thermodynamic stability of bulk Co2CrAl and all 2D phases of the compound. According to our electronic calculations, the bulk phase of Co2CrAl is a half-metal whose values of magnetic moment and spin polarization is 3 μB and 100% at the Fermi level, respectively. Besides, α and ϒ phases show the metal behavior for both spin directions in all imposed approximations. Finally, β phase exhibits different magnetic properties for different approximations. From 3eV to 2eV, GGA and GGA+U reveal the magnetic anisotropic and isotropic nature. Besides, an extremely anisotropic nature is observed at the Fermi level by GGA+U+mbJ.