  We give a conditional lower bound on the number of non-trivial simple zeros
for the Dedekind zeta function $\zeta_{K}(s)$, where $K$ is a quadratic number
field. The conditional result is given by assuming a Lindel\"of on average (in
the $L^{6}$ sense) for both $\zeta(s)$ and $L(s,\chi)$, which can be seen as a
stronger version of Conrey-Gonek-Ghosh's \cite{c} conditional result. This
improves upon the work of Wu and Zhao \cite{Zhao}, who had a similar result.
