  In this paper, we investigate holographic superconductors dual to
asymptotically anti-de Sitter black holes in an Einstein-Maxwell-scalar model
with a non-minimal coupling between the scalar and Maxwell fields. In the probe
limit, it shows that the scalar condensate occurs below the critical
temperature $T_{c}$, and decreases with the increase of the coupling constant
$\alpha$. On the other hand, the the critical temperature $T_{c}$ increases as
the coupling constant $\alpha$ grows. We also calculate the optical
conductivity of the holographic superconductor, and observe that a gap forms
below $T_{c}$. Interestingly, the non-minimal coupling can lead to a spike
occurring in the gap at a low temperature.
