Recent advances in non-radiative wireless power transfer (WPT) technique essentially relying on magnetic resonance and near-field coupling have successfully enabled a wide range of applications. However, WPT systems based on double resonators are severely limited to short- or mid-range distance, due to the deteriorating efficiency and power with long transfer distance. WPT systems based on multi-relay resonators can overcome this problem, which, however, suffer from sensitivity to perturbations and fabrication imperfections. Here, we experimentally demonstrate a concept of topological wireless power transfer (TWPT), where energy is transferred efficiently via the near-field coupling between two topological edge states localized at the ends of a one-dimensional radiowave topological insulator. Such a TWPT system can be modelled as a parity-time-symmetric Su-Schrieffer-Heeger (SSH) chain with complex boundary potentials. Besides, the coil configurations are judiciously designed, which significantly suppress the unwanted cross-couplings between nonadjacent coils that could break the chiral symmetry of the SSH chain. By tuning the inter- and intra-cell coupling strengths, we theoretically and experimentally demonstrate high energy transfer efficiency near the exceptional point of the topological edge states, even in the presence of disorder. The combination of topological metamaterials, non-Hermitian physics, and WPT techniques could promise a variety of robust, efficient WPT applications over long distances in electronics, transportation, and industry.