  Let $k$ and $n$ be two nonnegative integers with $n\equiv0$ (mod 2), and let
$G$ be a graph of order $n$ with a 1-factor. Then $G$ is said to be
$k$-extendable for $0\leq k\leq\frac{n-2}{2}$ if every matching in $G$ of size
$k$ can be extended to a 1-factor. In this paper, we first establish a lower
bound on the signless Laplacian spectral radius of $G$ to ensure that $G$ is
$k$-extendable. Then we create some extremal graphs to claim that all the
bounds derived in this article are sharp.
