generalize the slice spaces \[in this case, $\Phi(\tau):=\tau^r$ for any $\tau\in [0,\fz)$ with $r\in(0,\infty)$\] recently defined and studied by Auscher and Mourgoglou [@am] (the case $r=2$) as well as by Auscher and Prisuelos-Arribas [@ap]. Based on these Orlicz-slice spaces, we then introduce a new kind of Hardy-type spaces, the Orlicz-slice Hardy spaces $(HE_\Phi^q)_t(\rn)$, via the radial maximal functions. This new scale of Orlicz-slice Hardy spaces contains the variant of the Orlicz-Hardy space, $H_*^\Phi(\rn)$ \[in this case, $q=t=1$\], of Bonami and Feuto [@bf] as well as the Hardy-amalgam space \[in this case, $t=1$ and $\Phi(\tau):=\tau^p$ for any $\tau\in [0,\fz)$ with $p\in (0,\fz)$\] of Ablé and Feuto [@af1] as special cases. Their characterizations via the atom, the molecule, various maximal functions, the Poisson integral and the Littlewood-Paley functions are also obtained. As an application of these characterizations, we then establish finite atomic characterizations of Orlicz-slice Hardy spaces, which further induce a description of their dual spaces and a criterion on the boundedness of sublinear operators from these Orlicz-slice Hardy spaces into a quasi-Banach space. Then, applying this criterion, we obtain the boundedness of $\delta$-type Calderón-Zygmund operators on these Orlicz-slice Hardy spaces. Moreover, the relations between the Orlicz-slice space and the Orlicz-slice Hardy 