  In this paper we re-investigate the model of the anti-de Sitter gravity
coupled to Maxwell and charged scalar fields, which has been studied as the
gravitational dual to a superconductor for a long time since the famous work
[Phys.\ Rev.\ Lett.\ {\bf 101}, 031601 (2008)]. By numerical method, we present
a novel family of solutions of holographical superconductor with excited
states, and find there exists a lower critical temperature in the corresponding
excited state. Moreover, we study the condensate and conductivity in the
excited states. It is very interesting that the conductivity $\sigma$ of each
excited state has an additional pole in $\text{Im}[\sigma]$ and a delta
function in $\text{Re}[\sigma]$ arising at the low temperature inside the gap,
which is just the evidence of the existence of excited states.
