  Given a number field $K$ of degree $n_K$ and with absolute discriminant
$d_K$, we obtain an explicit bound for the number $N_K(T)$ of non-trivial zeros
(counted with multiplicity), with height at most $T$, of the Dedekind zeta
function $\zeta_K(s)$ of $K$. More precisely, we show that for $T \geq 1$, $$
\Big| N_K (T) - \frac{T}{\pi} \log \Big( d_K \Big( \frac{T}{2\pi
e}\Big)^{n_K}\Big)\Big|
  \le 0.228 (\log d_K + n_K \log T) + 23.108 n_K + 4.520, $$ which improves
previous results of Kadiri and Ng, and Trudgian. The improvement is based on
ideas from the recent work of Bennett $et$ $al.$ on counting zeros of Dirichlet
$L$-functions.
