The rapid advancement of gravitational wave astronomy in recent years has paved the way for the burgeoning development of black hole spectroscopy, which enhances the possibility of testing black holes by their quasinormal modes (QNMs). In this paper, the axial gravitational perturbations and the QNM frequencies of black holes in the hybrid metric-Palatini gravity (HMPG) are investigated. The HMPG theory is characterized by a dynamical scalar degree of freedom and is able to explain the late-time accelerating expansion of the universe without introducing any textit{ad hoc} screening mechanism to preserve the dynamics at the Solar System scale. We obtain the master equation governing the axial gravitational perturbations of the HMPG black holes and calculate the QNM frequencies. Moreover, in the scrutiny of the black holes and their QNMs, we take into account the constraints on the model parameters based on the post-Newtonian analysis, and show how the QNM frequencies of the HMPG black holes would be altered in the observationally consistent range of parameter space.
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