Let $K$ be a quadratic number field. We study the simple zeros of the Dedekind zeta function $zeta_K(s)$ in the region $mathcal{R}={s=sigma+it: 0<sigma<1}$. Denote by $N_K'(T)$ the number of simple zeros $rho=sigma+itin mathcal{R}$ of $zeta_K(s)$ with $0<t<T$. We established a new lower bound for $N_K'(T)$ when $T$ is sufficiently large. Our bound improves upon the classical result of Conrey, Ghosh and Gonek. This talk is based on a joint work with Xiaosheng Wu.