  Let $p,q\in [1,\infty]$, $\alpha\in{\mathbb{R}}$, and $s$ be a non-negative
integer. In this article, the authors introduce a new function space
$\widetilde{JN}_{(p,q,s)_{\alpha}}(\mathcal{X})$ of John-Nirenberg-Campanato
type, where $\mathcal{X}$ denotes $\mathbb{R}^n$ or any cube $Q_{0}$ of
$\mathbb{R}^n$ with finite edge length. The authors give an equivalent
characterization of $\widetilde{JN}_{(p,q,s)_{\alpha}}(\mathcal{X})$ via both
the John-Nirenberg-Campanato space and the Riesz-Morrey space. Moreover, for
the particular case $s=0$, this new space can be equivalently characterized by
both maximal functions and their commutators. Additionally, the authors give
some basic properties, a good-$\lambda$ inequality, and a John-Nirenberg type
inequality for $\widetilde{JN}_{(p,q,s)_{\alpha}}(\mathcal{X})$.
