  In this paper, we study Noetherian local rings $R$ having a finite number of
trace ideals. We proved that such rings are of dimension at most two.
Furthermore, if the integral closure of $R/H$, where $H$ is the zeroth local
cohomology, is equi-dimensional, then the dimension of $R$ is at most one. In
the one-dimensional case, we can reduce to the situation that rings are
Cohen-Macaulay. Then, we give a necessary condition to have a finite number of
trace ideals in terms of the value set obtained by the canonical module. We
also gave the correspondence between trace ideals of $R$ and those of the
endomorphism algebra of the maximal ideal of $R$ when $R$ has minimal
multiplicity.
