The gluon self-coupling in Quantum Chromodynamics (QCD), the theory of strong interactions, suggests the existence of bound states of gauge bosons, the so-called glueballs. In pure Yang-Mills theory, these are the only possible particle states. In the presence of quarks, the situation is more difficult, because glueball states can mix with quark-antiquark states and their existence is thus hard to confirm experimentally. An outstanding problem is to calculate theoretical predictions of glueball couplings and decay rates from first principles, which will crucially important in identifying glueball states in the experiment. Such calculations are difficult and fraught with uncertainties in the conventional approach using lattice gauge theories. A different approach to such calculations is gauge/gravity duality. In this work previous calculation of glueball decay rates in the Sakai-Sugimoto model, which is a specific string-theoretic realization of gauge/gravity duality based on D8 and anti-D8 probe branes in Witten's holographic model of nonsupersymmetric Yang-Mills theory, are reviewed and extended. This model reproduces various features of low-energy QCD such as chiral symmetry breaking and yields a good approximation to meson and glueball mass spectra. In particular the pseudovector glueball, which is even under parity but odd under charge conjugation, is considered. It is dual to fluctuations in the background Kalb-Ramond field. Calculating the decay rates using the highly constrained Chern-Simons action of the D8 branes one finds a surprisingly large decay width. The decay pattern comprises decays into two and three pseudoscalar and vector mesons.