  In this work, we explore the possibilities of producing Axion-Like Particles
(ALPs) in a future $e^-p$ collider. Specifically, we focus on the proposed
Large Hadron electron collider (LHeC), which can achieve a center-of-mass
energy of $\sqrt{s} \approx 1.3$~TeV, enabling us to probe relatively high ALP
masses with $m_a \lesssim 300$~GeV. The production of ALPs can occur through
various channels, including $W^+W^-$, $\gamma\gamma$, $ZZ$, and
$Z\gamma$-fusion within the collider environment. To investigate this, we
conduct a comprehensive analysis that involves estimating the production cross
section and constraining the limits on the associated couplings of ALPs, namely
$g_{WW}$, $g_{\gamma\gamma}$, $g_{ZZ}$, and $g_{Z\gamma}$. To achieve this, we
utilize a multiple-bin $\chi^2$ analysis on sensitive differential
distributions. Through the analysis of these distributions, we determine upper
bounds on the associated couplings within the mass range of 5~GeV $\leq m_a
\leq$ 300~GeV. The obtained upper bounds are of the order of ${\cal
O}(10^{-1})$ for $g_{\gamma\gamma}$ ($g_{WW}$, $g_{ZZ}$, $g_{Z\gamma}$) in $m_a
\in$~[5, 200 (300)]~GeV considering an integrated luminosity of 1~ab$^{-1}$.
Furthermore, we compare the results of our study with those obtained from other
available experiments. We emphasize the limits obtained through our analysis
and showcase the potential of the LHeC in probing the properties of ALPs.
