Abstract: By the line element of relativistic velocity space,the hyperbolic geometry property of the space is particularly discussed.It is proved that the gather of relativistic velocity constitutes Klein-Beltrami model of hyperbolic geometry.General expression of Thomas precession is directly derived.It is indicated that the Thomas precession is the direct evidence of hyperbolic geometric property of relativistic velocity space.In comparison with Poincare model of hyperbolic geometry,the Klein-Beltrami model can directly explain the laws of relativistic velocity,because the coordinates in the model is usual velocity.

Key words: special relativity, relativistic velocity space, hyperbolic geometry, Thomas precession