In the 3-dimensional de Sitter Space S31, a surface is said to be a spherical (resp. hyperbolic or parabolic) rotation surface, if it is a orbit of a regular curve under the action of the orthogonal transformations of the 4-dimensional Minkowski space E4 1 which leave a timelike (resp. spacelike or degenerate) plane pointwise fixed. In this paper, we give all spacelike and timelike Weingarten rotation surfaces in S31.