We have revisited and refined the high-pressure elastic properties of body-centered-cubic Ta using the accurate all-electron full potential linearized augmented plane wave method (FP-LAPW) within the framework of density functional theory (DFT). Based on the total energy calculations, we first deduced the accurate static equation of state (EOS) of Ta. Then we derived the elastic constants, C11, C12, and C44 under pressure up to 500 GPa using the pressure-correction method which corrected the previous method theoretically, and the calculated elastic constants agree well with experiment under high pressure. From the accurately determined elastic constants, we also discussed the elastic anisotropy and the sound velocities of Ta at high pressure. The predicted Debye temperature at 0 GPa and 0 K is in good agreement with experiment, and the Debye temperature increases monotonously as pressure increases.