  We construct a holographic model with Weyl corrections in five dimensional
spacetime. In particular, we introduce a coupling term between the axion fields
and the Maxwell field such that the momentum is relaxed even in the probe limit
in this model. We investigate the Drude behavior of the optical conductivity in
low frequency region. It is interesting to find that the incoherent part of the
conductivity is suppressed with the increase of the axion parameter $k/T$,
which is in contrast to other holographic axionic models at finite density.
Furthermore, we study the superconductivity associated with the condensation of
a complex scalar field and evaluate the critical temperature for condensation
in both analytical and numerical manner. It turns out that the critical
temperature decreases with $\tilde{k}$,indicating that the condensation becomes
harder in the presence of the axions, while it increases with Weyl parameter
$\gamma$. We also discuss the change of the gap in optical conductivity with
coupling parameters. Finally, we evaluate the charge density of the superfluid
in zero temperature limit, and find that it exhibits a linear relation with
$\tilde{\sigma}_{DC}(\tilde{T_c})\tilde{T_c}$, such that a modified version of
Homes' law is testified.
