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 backreaction from the flavor fennions is taken into account. For both cases, we could find the expected Roberge-Weiss (RW) transitions. In the case of the backreacted solution, a bound of the color number N-c is found to produce the RW periodicity. It is given as N-c >= 1.2. Furthermore, we could assure the validity of this extended model by comparing our result with that of the lattice QCD near mu(I) =0.