  Aether theory is introduced to implement the violation of the Lorentz
invariance in general relativity. For this purpose a unit timelike vector field
introduced to theory in addition to the metric tensor. Aether theory contains
four free parameters which satisfy some inequalities in order that the theory
to be consistent with the observations. We show that the G{\" o}del type of
metrics of general relativity are also exact solutions of the Einstein-aether
theory. The only field equations are the 3-dimensional Maxwell field equations
and the parameters are left free except $c_{1}-c_{3}=1$.
