The harmonic index $H(G)$ of a graph $G$ is the sum of the weights $\frac2{d(u)+d(v)}$ of all edges $uv$ of $G$, where $d(u)$ denotes the degree of a vertex $u$ in $G$. In this work, a lower bound for the harmonic index of a graph with minimum degree at least three is obtained and the corresponding extremal graph is characterized.