The structural, elastic and thermodynamic characteristics of CeGa2 compound in the AlB2 (space group: P6/mmm) and the omega trigonal (space group: P-3m1) type structures are investigated using the methods of density functional theory within the generalized gradient approximation (GGA). The thermodynamic properties of the considered structures are obtained through the quasi-harmonic Debye model. The results on the basic physical parameters, such as the lattice constant, the bulk modulus, the pressure derivative of bulk modulus, the phase-transition pressure (P
t) from P6/mmm to P-3m1 structure, the second-order elastic constants, Zener anisotropy factor, Poisson’s ratio, Young’s modulus, and the isotropic shear modulus are presented. In order to gain further information, the pressure and temperature-dependent behavior of the volume, the bulk modulus, the thermal expansion coefficient, the heat capacity, the entropy, Debye temperature and Grüneisen parameter are also evaluated over a pressure range of 0–6 GPa and a wide temperature range of 0–1800 K. The obtained results are in agreement with the available experimental and the other theoretical values.