  In this paper, we have studied the effect of Born-Infeld electrodynamics in
holographic $p$-wave superconductors with massive vector condensation. We have
analysed this model in the probe limit using a variational method known as the
St\"urm-Liouville eigenvalue approach. For this $p$-wave holographic
superconductor model, we have calculated the critical temperature $T_{c}$ as
well as the value of the condensation operator for two different choices of
$m^{2}$. We have also pointed out the similarities and dissimilarities between
this model for $m^{2} = 0$ and $p$-wave holographic superconductor model
constructed out of Einstein-Yang-Mills theory. We have then computed the
conductivity of these holographic superconductor models using a self-consistent
approach and have shown that the DC conductivity diverges.
