  The spacetime homogeneous G\"odel-type spacetimes which have four classes of
metrics are studied according to their matter collineations. The obtained
results are compared with Killing vectors and Ricci collineations. It is found
that these spacetimes have infinite number of matter collineations in
degenerate case, i.e. det$(T_{ab}) = 0$, and do not admit proper matter
collineations in non-degenerate case, i.e. det$(T_{ab}) \ne 0$. The degenerate
case has the new constraints on the parameters $m$ and $w$ which characterize
the causality features of the G\"odel-type spacetimes.
