Effects　of　pressure　on　lattice　parameters,　electronic,　thermodynamic　and　mechanical　properties　of　the　fully　ordered　Ti2AlNb　orthorhombic　phase　were　studied　using　first-principles　calculations　based　on　density　functional　theory　(DFT).　The　bonding　nature　for　ordering　orthorhombic　Ti2AlNb　was　revealed　quantitatively　through　the　electronic　structure　analyzing.　The　external　pressures　play　limited　roles　in　the　elastic　anisotropy　of　the　alloy　due　to　the　outstanding　dynamical　and　mechanical　stabilities　under　pressure.　However,　the　shear　modulus　of　O　phase　manifests　anisotropic,　where　{010}　shear　planes　are　the　easiest　planes　to　cleave　among　the　principal　planes　under　all　pressures.　The　heat　capacities,　volume　expansions　and　thermal　expansion　coefficients　were　calculated　using　the　quasi-harmonic　approximation　model　based　on　the　phonon　dispersion　curves.　Meanwhile,　the　bulk　modulus,　Young＇s　modulus,　shear　modulus　and　the　hardness　are　promptly　enhanced　under　pressure.　The　predicted　results　give　hints　to　design　Ti2AlNb-based　alloy　as　high-pressure　applications.