The harmonic index $H(G)$ of a graph $G$ is defined as the sum of 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 paper, we first present a sharp lower bound on the harmonic index of bicyclic conjugated molecular graphs (bicyclic graphs with perfect matching). Also a sharp lower bound on the harmonic index of bicyclic graphs is given in terms of the order and given size of matching.