  Studying the color superconductivity (CSC) phase is essential to understand
the physics in the core of the neutron stars which is the only known context
where the CSC phase might appear due to the gravitational force squeezing the
matter to a sufficiently high density. We propose a simple holographic dual
description of the CSC phase transition in the realistic Yang-Mills theory with
the power-law Maxwell field. We find the CSC phase transition with the large
color number in the deconfinement phase, which is not found in the case of the
usual Maxwell field, if the power parameter characterizing for the power-law
Maxwell field is sufficiently lower than one but above $1/2$ and the chemical
potential is above a critical value. However, the power parameter is not
arbitrary below one because when this parameter is sufficiently far away from
one it leads to the occurrence of the CSC state in the confinement phase which
is not compatible with a nonzero vacuum expectation value of the color
nonsinglet operator.
