  Let $\alpha\in\mathbb R^n$, $t\in(0,\infty)$, $p\in(0,\infty]$,
$r\in(1,\infty)$ and $q\in[1,\infty]$. We introduce the homogeneous Herz-slice
space $(\dot KE_{q,r}^{\alpha,p})_t(\mathbb R^n)$, the non-homogeneous
Herz-slice space $(KE_{q,r}^{\alpha,p})_t(\mathbb R^n)$ and show some
properties of them. As an application, the bounds for the Hardy--Littlewood
maximal operator on these spaces is considered.
