The spontaneous emission properties of the two-level atoms placed near a topological insulator (TI) slab with a finite thickness or inside its cavity are investigated. The spontaneous emission rates of the dipole parallel or perpendicular to the material boundary are expressed via the dyadic Green function. The reflection matrix of this slab is calculated based on the multiple reflection theory, and the various factors which influence the spontaneous emission rate are numerically calculated and analyzed. The research results show that, when the dissipation is ignored, the spontaneous emission rate of the parallel dipole is suppressed, however, that of the perpendicular dipole is enhanced. When the dissipation of the slab or its cavity is included, the TI can effectively suppress the spontaneous emission rate of the atoms and make all of the decays of atoms near it along any diploe directions suppressed.