Axion-like particles (ALPs) provide a promising direction in the search for new physics, while a wide range of models incorporate ALPs. We point out that future neutrino experiments, such as DUNE, possess competitive sensitivity to ALP signals. The high-intensity proton beam impinging on a target can not only produce copious amounts of neutrinos, but also cascade photons that are created from charged particle showers stopping in the target. Therefore, ALPs interacting with photons can be produced (often energetically) with high intensity via the Primakoff effect and then leave their signatures at the near detector through the inverse Primakoff scattering or decays to a photon pair. Moreover, the high-capability near detectors allow for discrimination between ALP signals and potential backgrounds, improving the signal sensitivity further. We demonstrate that a DUNE-like detector can explore a wide range of parameter space in ALP-photon coupling $g_{agamma}$ vs ALP mass $m_a$, including some regions unconstrained by existing bounds; the cosmological triangle will be fully explored and the sensitivity limits would reach up to $m_asim3-4$ GeV and down to $g_{agamma}sim 10^{-8} {rm GeV}^{-1}$.