A graph $\Gamma$ is said to be vertex-transitive or edge- transitive if the automorphism group of $Gamma$ acts transitively on $V(\Gamma)$ or $E(\Gamma)$, respectively. Let $\Gamma=Cay(G,S)$ be a Cayley graph on $G$ relative to $S$. Then, $\Gamma$ is said to be normal edge-transitive, if $N_{Aut(\Gamma)}(G)$ acts transitively on edges. In this paper, the eigenvalues of normal edge-transitive Cayley graphs of the groups $D_{2n}$ and $T_{4n}$ are given.
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