  In this paper we study Weyl fermions in a family of G\"odel-type geometries
in Einstein general relativity. We also consider that these solutions are
embedded in a topological defect background. We solve the Weyl equation and
find the energy eigenvalues and eigenspinors for all three cases of
G\"odel-type geometries where a topological defect is passing through them. We
show that the presence of a topological in these geometries contributes to
modification of the spectrum of energy. The energy zero modes for all three
cases of the G\"odel geometries are discussed.
