  Similar to the definition of Dupin hypersurface in Riemannian space forms, we
define the spacelike Dupin hypersurface in Lorentzian space forms. As conformal
invariant objects, spacelike Dupin hypersurfaces are studied in this paper
using the framework of conformal geometry. Further we classify the spacelike
Dupin hypersurfaces with constant M\"{o}bius curvatures, which are the
partition ratio of the principal curvatures of the spacelike Dupin
hypersurface.
