We performed a first-principles study of the electronic, elastic, and thermal properties of the rareearth hexaboride CeB6 using the local density approximation (LDA) in consideration of the effective onsite Coulomb parameter Ueff. To systemically evaluate the effect of Ueff on the structure of the material, the dependences of the lattice parameter a0 and bulk modulus B on Ueff were examined in the framework of the LDA+U and GGA(PBE)+U scheme. We obtained a lattice constant a0, elastic constants Cij , and a bulk modulus B at 0 K and 0 GPa that were in good agreement with the experimental results and other theoretical findings. We focused on the electronic structure by analyzing the variation of the density of states with different Ueff values and pressures, which indicates the metallic characteristic of CeB6. Interestingly, the effect of high pressure was similar to that of increasing Ueff , as the peaks at the bottom of the conduction band moved to the high-energy region in both cases. The elastic constants Cij , bulk modulus B, shear modulus G, Young’s modulus E, shear-sound velocity VS, and longitudinal-sound velocity VL were calculated from 0 to 120 GPa. Additionally, the Debye temperature ΘD and elastic Debye temperature ΘE were systematically calculated using the thermodynamic methods in the range of 0–100 GPa. This research may provide a comprehensive understanding of the Kondo compound CeB6 and similar rare-earth hexaborides.