The spin–orbit torque induced by a topological insulator (TI) is theoretically examined for spin wave generation in a neighboring antiferromagnetic thin film. The investigation is based on the micromagnetic simulation of Néel vector dynamics and the analysis of transport properties in the TI. The results clearly illustrate that propagating spin waves can be achieved in the antiferromagnetic thin-film strip through localized excitation, traveling over a long distance. The oscillation amplitude gradually decays due to the non-zero damping as the Néel vector precesses around the magnetic easy axis with a fixed frequency. The frequency is also found to be tunable via the strength of the driving electrical current density. While both the bulk and the surface states of the TI contribute to induce the effective torque, the calculation indicates that the surface current plays a dominant role over the bulk counterpart except in the heavily degenerate cases. Compared to the more commonly applied heavy metals, the use of a TI can substantially reduce the threshold current density to overcome the magnetic anisotropy, making it an efficient choice for spin wave generation. The Néel vector dynamics in the nano-oscillator geometry are examined as well.