  Inspired by the definition of $\bf{t}$-spread monomial ideals, in this paper,
we introduce $\bf{t}$-spread $d$-partite hypergraph $K^{\bf t}_V$ and study its
edge ideal $I(K^{\bf t}_V)$. We prove that $I(K^{\bf t}_V)$ has linear
quotients, all powers of $I(K^{\bf t}_V)$ have linear resolution and the Rees
algebra of $I(K^{\bf t}_V)$ is a normal Cohen-Macaulay domain. It is also shown
that $I(K^{\bf t}_V)$ is normally torsion-free and a complete characterization
of Cohen-Macaulay $S/I(K^{\bf t}_V)$ is given.
