  We construct the simplest gravitational dual model of a superconductor on
Q-lattices. We analyze the condition for the existence of a critical
temperature at which the charged scalar field will condense. In contrast to the
holographic superconductor on ionic lattices, the presence of Q-lattices will
suppress the condensate of the scalar field and lower the critical temperature.
In particular, when the Q-lattice background is dual to a deep insulating
phase, the condensation would never occur for some small charges. Furthermore,
we numerically compute the optical conductivity in the superconducting regime.
It turns out that the presence of Q-lattice does not remove the pole in the
imaginary part of the conductivity, ensuring the appearance of a delta function
in the real part. We also evaluate the gap which in general depends on the
charge of the scalar field as well as the Q-lattice parameters. Nevertheless,
when the charge of the scalar field is relatively large and approaches the
probe limit, the gap becomes universal with $\omega_g \simeq 9T_c$ which is
consistent with the result for conventional holographic superconductors.
