  We have studied perturbations of scalar and spinor field in the background of
three dimensional G\"{o}del black hole. The wave equations are shown to be
exactly solvable in terms of hypergeometric functions. The quasinormal modes
are analytically calculated by imposing the Dirichlet boundary condition at
spatial infinity, which are shown to be of the same form in both cases. By
considering the physical interpretation of quasinormal modes, we obtain the
consistent transition frequencies from the quasinormal modes of scalar and
spinor field. As an application of quasinormal modes, we have also investigated
the area and entropy quantization of three dimensional G\"{o}del black hole. By
choosing the conserved mass of G\"{o}del black hole properly, the entropy
spectrum are shown to be equally-spaced.
