We report the magnetic and magnetocaloric properties of the antiferromagnetic intermetallic compound CeMg, focusing on its coupled magnetic and structural phase transition within first-order processes. Our study utilizes a model Hamiltonian incorporating interactions such as: crystalline electrical field, intra and inter sublattice exchange interactions, as well as quadrupolar and magnetoelastic to elucidate the behavior of CeMg. Through simulation, we predict and discuss both normal and inverse magnetocaloric effects, providing insights into the magnetocaloric behavior under different magnetic field directions. These findings contribute to a deeper understanding of the complex magnetism in CeMg and lay the groundwork for future experimental investigations.