Strong coupling between cavity photons and various excitations in condensed matters boosts the field of light-matter interaction and generates several exciting sub-fields, such as cavity optomechanics and cavity magnon polariton. Axion quasiparticles, emerging in topological insulators, were predicted to strongly couple with the light and generate the so-called axion polariton. Here, we demonstrate that there arises a gapless level attraction in cavity axion polariton of antiferromagnetic topological insulators, which originates from a nonlinear interaction between axion and the odd-order resonance of cavity. Such a novel level attraction is essentially different from conventional level attractions with the mechanism of either a linear coupling or a dissipation-mediated interaction, and also different from the level repulsion induced by the strong coupling in common polaritons. Our results reveal a new mechanism of level attractions, and open up new roads for exploring the axion polariton with cavity technologies. They have potential applications for quantum information and dark matter research.