article. Recall that the boundedness of the Hardy-Littlewood maximal operator on the amalgam space $(L^p,\ell^q)(\rn)$ with $p,\,q\in(1,\infty)$ was obtained in [@chh]. However, the approach used in [@chh] for $(L^p,\ell^q)(\rn)$ is no longer feasible for $(E_\Phi^q)_t(\rn)$ because the quasi-norm $\|\cdot\|_{L^\Phi(\rn)}$ cannot be represented as an integral and hence cannot apply the weighted boundedness of the Hardy-Littlewood maximal operator. To overcome this obstacle, we employ a different method, namely, we first establish a generalization of [@ap Lemma 4.1] via replacing the maximal function and $L^r(\rn)$ norm therein, respectively, by the vector-valued maximal function and $L^\Phi(\rn)$ norm here (see Lemma \[mm\] below), which plays a key role in establishing the Fefferman-Stein vector-valued inequality for the Hardy-Littlewood maximal operator on $(E_\Phi^q)_t(\rn)$ (see the proof of Theorem \[main\]); from Theorem \[main\], we immediately induce the desired boundedness of the Hardy-Littlewood maximal operator on $(E_\Phi^q)_t(\rn)$. We also point out that the proof of Theorem \[dual\] strongly depends on Proposition \[th2\] and the well-known dual spaces of Orlicz-amalgam spaces. Moreover, in Lemma \[ballproof\] below, we further prove that the Orlicz-slice spaces $(E_\Phi^q)_t(\rn)$ are ball quasi-Banach function spaces considered in [@ykds] and hence all results from [@ykds] are applicable to $(E_\Phi^q)_t(\rn)$.

In Section \[s3\], based on the Orlicz-slice 