  A wheel graph is a graph formed by connecting a single vertex to all vertices
of a cycle. A graph is called wheel-free if it does not contain any wheel graph
as a subgraph. In 2010, Nikiforov proposed a Brualdi-Solheid-Tur\'{a}n type
problem: what is the maximum spectral radius of a graph of order $n$ that does
not contain subgraphs of particular kind. In this paper, we study the
Brualdi-Solheid-Tur\'{a}n type problem for wheel-free graphs, and we determine
the maximum (signless Laplacian) spectral radius of a wheel-free graph of order
$n$. Furthermore, we characterize the extremal graphs.
