  A potential thermoelectric material CuAlO$_2$ is theoretically studied. We
first construct a model Hamiltonian of CuAlO$_2$ based on the first principles
band calculation, and calculate the Seebeck coefficient. Then, we compare the
model with that of a well-known thermoelectric material Na$_x$CoO$_2$, and
discuss the similarities and the differences. It is found that the two
materials are similar from an electronic structure viewpoint in that they have
a peculiar pudding-mold type band shape, which is advantageous as
thermoelectric materials. There are however some differences, and we analyze
the origin of the difference from a microscopic viewpoint. The band shape of
CuAlO$_2$ is found to be even more ideal than that of Na$_x$CoO$_2$, and we
predict that once a significant amount of holes is doped in CuAlO$_2$,
thermoelectric properties (especially the power factor) even better than that
of Na$_x$CoO$_2$ can be expected.
