Based on the theory of large deformation and using the differential geometry. The paper derived the relationship of strain and displacement for spatial curved beams, taking into account the longitudinal strains and torsion strains, but neglecting the effects of shear, moment of inertia and warping. The Hamilton variation principle was used to derive the nonlinear dynamics equations of spatial curved beam under three-displacement- freedom and three-rotation-freedom, which can be degenerated to linear dynamics equations of planar circular arch, and their results were compared with the results in literatures. The nonlinear dynamics equations provide a reliable foundation for analysis of the nonlinear dynamics of curved beam.