  In this letter we construct the St\"{u}ckelberg holographic superconductor
with Weyl corrections. Under such corrections, the Weyl coupling parameter
$\gamma$ plays an important role in the order of phase transitions and the
critical exponents of second order phase transitions. So do the model
parameters $c_{\alpha}$, $\alpha$ and $c_{4}$. Moreover, we show that the Weyl
coupling parameter $\gamma$ and the model parameters $c_{\alpha}$, $\alpha$,
$c_{4}$ which together control the size and strength of the conductivity
coherence peak and the ratio of gap frequency over critical temperature
$\omega_{g}/T_{c}$.

High Energy Physics - Theory;General Relativity and Quantum Cosmology