  In this paper, we have constructed a bottom-up holographic model for the
color superconductivity (CSC) of the Yang-Mills theory in the context of
Einstein-Gauss-Bonnet (EGB) gravity, which allows to study the CSC phase with
the color number $N_c\geq2$. We analyze the Cooper pair condensate in the
deconfinement and confinement phases which are dual to the planar GB-RN-AdS
black hole and GB-AdS soliton, respectively, with including the backreaction of
the matter part. By examining the breakdown of the Breitenlohner-Freedman bound
in the background of the planar GB-RN-AdS black hole, we find that the upper
bound of the color number with the GB coupling parameter $\alpha>0$ is low in
comparison to Einstein gravity where the CSC phase for $N_c\geq2$ is not
realized. But, with the $\alpha<0$ case, it is possible to observe the Cooper
pair condensate for $N_c\geq2$ with the reasonable amplitude of $\alpha$. This
is confirmed and the corresponding phase diagram is found by solving
numerically the equations of motion for the gravitational system. In addition,
we show that the CSC phase disappears in the confinement phase for the
amplitude of $\alpha$ below a certain value which means that beyond that value
it may lead to the breakdown region of the EGB gravity in investigating the CSC
phase.
