We investigate the photon-ALP (axion-like particle) oscillation effect on TeV gamma-ray spectral irregularities from the uncertain redshift active galactic nuclei (AGN) VER J0521+211. The gammaray spectra are measured by the collaborations Fermi-LAT and VERITAS with the three flux states in 2013 and 2014. We set the combined constraints on the ALP parameter (ma, gaγ) space with these states and test the extragalactic background light (EBL) absorption effect on ALP constraints with the four redshift upper limit scenarios of VER J0521+211. The 3σ photon-ALP combined constraints set by VER J0521+211 are roughly at gaγ 2.3 × 10 −11 GeV −1 for ma 5 × 10 −8 eV. We find no clear connection between the redshift upper limit scenarios and the photon-ALP constraints.