Let \(\Delta(G)\) be the maximum degree of a graph \(G\), and let \(\mathcal{U}(n, \Delta)\) be the set of all unicyclic graphs on \(n\) vertices with fixed maximum degree \(\Delta\). Among all the graphs in \(\mathcal{U}(n, \Delta)\) (\(\Delta \geq \frac{n+3}{2}\)), we characterize the graph with the maximal spectral radius. We also prove that the spectral radius of a unicyclic graph \(G\) on \(n\) (\(n \geq 30\)) vertices strictly increases with its maximum degree when \(\Delta(G) \geq \lceil\frac{7n}{9}\rceil + 1\).