  Holographic superconductors containing a non-minimal derivative coupling for
scalar field in a regular phantom plane symmetric black hole have been
considered. We show that the parameter of the regular black hole $b$ as well as
the non-minimal derivative coupling parameter $\eta$ affect the formation of
the condensate as well as the conductivity in the superconductor. Moreover, $b$
has a critical value in which the critical temperature $T_c$ increases without
a bound. We argue that an unlimited critical temperature is an evidence that
high $T_c$ superconductor must be related to the absence of a singularity in
the bulk in the AdS/CFT context.
