  In this work, we calculate the sensitivities on the gauge-boson couplings
$g_{aZZ}$, $g_{aZ\gamma}$, and $g_{aWW}$ of an axion-like particle (ALP) that
one can achieve at the LHC with $\sqrt{s}=14$ TeV and integrated luminosities
of 300 fb$^{-1}$ (current run) and 3000 fb$^{-1}$ (High-Luminosity LHC). We
focus on the associated production processes $pp\to Za \to
(l^+l^-)(\gamma\gamma)$ and $pp\to W^\pm a \to (l^\pm \nu)(\gamma\gamma)$. We
show that better sensitivities on these gauge couplings can be achieved at the
LHC for $M_a = 1-100$ GeV, down to the level of $10^{-4}\,{\rm GeV}^{-1}$. In
conclusion, this study emphasizes the significance of the investigated channels
in constraining the ALP couplings at the LHC, offering valuable insights for
future experiments dedicated to ALP detection.
