  A connected graph $G$ is a cactus if any two of its cycles have at most one
common vertex. Let $\ell_n^m$ be the set of cacti on $n$ vertices with matching
number $m.$ S.C. Li and M.J. Zhang determined the unique graph with the maximum
signless Laplacian spectral radius among all cacti in $\ell_n^m$ with $n=2m$.
In this paper, we characterize the case $n\geq 2m+1$. This confirms the
conjecture of Li and Zhang(S.C. Li, M.J. Zhang, On the signless Laplacian index
of cacti with a given number of pendant vetices, Linear Algebra Appl. 436,
2012, 4400--4411). Further, we characterize the unique graph with the maximum
signless Laplacian spectral radius among all cacti on $n$ vertices.
