  In this paper, we study the effects of attractive correlation on the
topological insulator ($TI$) with topological flat-bands using an extended
attractive Kane-Mele-Hubbard model (KMHM). In the KMHM, we found a quantum
phase transition from $TI$ to the superconductor ($SC$) state upon the
increasing of the attractive Hubbard interaction $U$ at the mean field level.
This type of $SC$ phase transition is different from the traditional $SC$ phase
transition which develops from the gapless Fermi Liquid. Cooperon-type gapped
excitations exist in the $TI$ side near this type of $SC$ phase transition.
