Using first-principles calculations based on density functional theory, structural, elastic, electronic and thermoelectric properties of laves phase LaCo2 intermetallic compound with prototype MgCu2 are stated in this paper. The optimized lattice constant by structural optimization is found to be rationally compatible with the experimental lattice constant.  The Generalized Gradient Approximation (GGA) +Hubbard model was incorporated to evaluate the exact electronic structure. Elastic properties such as, elastic constants, bulk modulus B, shear modulus G, Young’s modulus E, and Poisson ratio ν have been determined using the Voigt–Reuss– Hill approximation. The ductility nature appears in both values of Cauchy pressure and Pugh’s ratio. The band structures and the Cauchy pressure show that the material behaves as metallic. In addition, semi-classical Boltzmann theory is used to verify the applicability of the material for thermoelectric applications. Calculations depict that the spin-up/down transport coefficients are temperature-dependent. It has been found that LaCo2 has a high Seebeck coefficient and therefore a large power factor.