The elastic and thermodynamic properties of CsCl-type structure LaB6 under high pressure are investigated by first-principles calculations based on plane-wave pseudopotential density functional theory method within the generalized gradient approximation (GGA). The calculated lattice parameters of LaB6 under zero pressure and zero temperature are in good agreement with the existing experimental data and other theoretical data. The pressure dependences of the elastic constants, bulk modulus B (GPa), shear modulus G, Young’s modulus E, elastic Debye temperature ΘE, Poisson ratio σ, compressional wave velocity VL and shear wave velocity VS are also presented. An analysis for the calculated elastic constants has been made to reveal the mechanical stability of LaB6 up to 14 GPa. The thermodynamic properties of the CsCl-type structure LaB6 are predicted using the quasi-harmonic Debye model. The variation of thermal expansion coefficient α, the variation of the heat capacity Cv are obtained systematically in the ranges of 0-14 GPa and 0-1500 K. At last, the pressure dependences of the density of states are also investigated.