  Let $p\in (1,\infty)$, $q\in[1,\infty)$, $\alpha\in [0,\infty)$ and $s$ be a
non-negative integer. In this article, the authors introduce the
John--Nirenberg-Campanato space $JN_{(p,q,s)_\alpha}(\mathcal{X})$, where
$\mathcal{X}$ is ${\mathbb R}^n$ or any closed cube $Q_0\subsetneqq{\mathbb
R}^n$, which when $\alpha=0$ and $s=0$ coincides with the $JN_p$-space
introduced by F. John and L. Nirenberg in the sense of equivalent norms. The
authors then give the predual space of $JN_{(p,q,s)_\alpha}(\mathcal{X})$ and a
John-Nirenberg type inequality of John--Nirenberg-Campanato spaces. Moreover,
the authors prove that the classical Campanato space serves as a limit space of
$JN_{(p,q,s)_\alpha}(\mathcal{X})$ when $p\to \infty$.
