In this paper, we obtain a certain rigidity property for Kleinian groups. This asserts that ifFandG(both non-elementary torsion-free Fuchsian groups) and [FF] = [GG],thenF=G(all equalities are taken in the sense of Möbius transformations). This result is connected to Torelli's theorem (for closed Riemann surfaces) and can be a step in understanding an equivalent for more general type of Riemann surfaces.