  In this paper, we study Noether gauge symmetries of geodesic motion for
geodesic Lagrangian of four classes of metrics of G\"{o}del-type spacetimes for
which we calculated the Noether gauge symmetries for all classes I-IV, and find
the first integrals of corresponding classes to derive a complete
characterization of the geodesic motion. Using the obtained expressions for
$\dot{t}, \dot{r}, \dot{\phi}$ and $\dot{z}$ of each classes I-IV which depends
essentially on two independent parameters $m$ and $w$, we explicitly integrated
the geodesic equations of motion for the corresponding G\"{o}del-type
spacetimes.
