  In this paper we investigate the model of the anti-de Sitter gravity coupled
to a Maxwell field and a free, complex scalar field, and construct a fully
back-reacted holographic model of superconductor with excited states. With the
fixed charge $q$, there exist a series of excited states of holographic
superconductor with the corresponding critical chemical potentials. The
condensates as functions of the temperature for the two operators
$\mathcal{O}_1$ and $\mathcal{O}_2$ of excited states are also studied. For the
optical conductivity in the excited states, we find that there exist the
additional peaks in the imaginary and real parts of the conductivity. Moreover,
the number of peaks corresponding to $n$-th excited state is equal to $n$.
