The relationship between the energy $ \varepsilon \left( G \right)$ and the $ {K_{1,s}}$-matching number $ {\mu _s}\left( G \right)$ of a graph $G$ was focused. It is proved that $ \varepsilon \left( G \right)$≥$ 2\sqrt s {\mu _s}\left( G \right)$. Furthermore, if each subgraph of $ G$ satisfies some special conditions, then $ \varepsilon \left( G \right)$≥$ 2\sqrt s {\mu _s}\left( G \right) + \dfrac{{\sqrt 5 }}{5}{c_1}\left( G \right)$, where $ {c_1}\left( G \right)$ is the number of odd cycles in $ G$. In addition, if the maximum degree of the tree $ T$ is no more than 3, then $ \varepsilon \left( T \right)$≥$ \left( {s + 1} \right){\mu _s}\left( T \right) - 1$.