  For a $hypergraph$ $\mathcal{G}=(V, E)$ consisting of a nonempty vertex set
$V=V(\mathcal{G})$ and an edge set $E=E(\mathcal{G})$, its $adjacency$ $matrix$
$\mathcal {A}_{\mathcal{G}}=[(\mathcal {A}_{\mathcal{G}})_{ij}]$ is defined as
$(\mathcal {A}_{\mathcal{G}})_{ij}=\sum_{e\in E_{ij}}\frac{1}{|e| - 1}$, where
$E_{ij} = \{e \in E : i, j \in e\}$. The $spectral$ $radius$ of a hypergraph
$\mathcal{G}$, denoted by $\rho(\mathcal {G})$, is the maximum modulus among
all eigenvalues of $\mathcal {A}_{\mathcal{G}}$. In this paper, among all
$k$-uniform ($k\geq 3$) supertrees with fixed number of vertices, the
supertrees with the maximum, the second maximum and the minimum spectral radius
are completely determined, respectively.
