  We investigate analytically the properties of the Weyl holographic
superconductor in the Lifshitz black hole background. We find that the critical
temperature of the Weyl superconductor decreases with increasing Lifshitz
dynamical exponent, $z$, indicating that condensation becomes difficult. In
addition, it is found that the critical temperature and condensation operator
could be affected by applying the Weyl coupling, $\gamma$. Moreover, we compute
the critical magnetic field and investigate its dependence on the parameters
$\gamma$ and $z$. Finally, we show numerically that the Weyl coupling parameter
$\gamma$ and the Lifshitz dynamical exponent $z$ together control the size and
strength of the conductivity peak and the ratio of gap frequency over critical
temperature $\omega_{g}/T_{c}$.
