  Let $S_{1}(m, d, k)$ be the $k$-uniform supertree obtained from a loose path
$P:v_{1}, e_{1}, v_{2}, \ldots,v_{d}, e_{d}, v_{d+1}$ with length $d$ by
attaching $m-d$ edges at vertex $v_{\lfloor\frac{d}{2}\rfloor+1}.$ Let
$\mathbb{S}(m,d,k)$ be the set of $k$-uniform supertrees with $m$ edges and
diameter $d$ and $q(G)$ be the signless Laplacian spectral radius of a
$k$-uniform hypergraph $G$. In this paper, we mainly determine $S_{1}(m,d,k)$
with the largest signless Laplacian spectral radius among all supertrees in
$\mathbb{S}(m,d,k)$ for $3\leq d\leq m-1$. Furthermore, we determine the unique
uniform supertree with the maximum signless Laplacian spectral radius among all
the uniform supertrees with $n$ vertices and pendent edges (vertices).
