  We extend a bottom up holographic model, which has been used in studying the
color superconductivity in QCD, to the imaginary chemical potential ($\mu_I$)
region, and the phase diagram is studied on the $\mu_I$-temperature (T) plane.
The analysis is performed for the case of the probe approximation and for the
background where the back reaction from the flavor fermions are taken into
account. For both cases, we could find the expected Roberge-Weiss (RW)
transitions. In the case of the back-reacted solution, a bound of the color
number $N_c$ is found to produce the RW periodicity. It is given as $N_c\geq
1.2$. Furthermore, we could assure the validity of this extended model by
comparing our result with the one of the lattice QCD near $\mu_I=0$.
