The detection of TeV gamma-ray bursts (GRBs) brought new opportunities to study the physics of particle acceleration at relativistic shocks. The H.E.S.S. telescopes recently observed very-highenergy (VHE) emission from a nearby low-luminosity GRB, GRB 190829A. Follow-up observations with, e.g., Swift-XRT, revealed unusual flare activities at ∼ 10 3 s, which can be caused by a longlasting central engine. We show that the VHE emission during the H.E.S.S. observation time is naturally produced in the external inverse-Compton (EIC) scenario, where seed photons supplied by the flares or other late-time dissipation are upscattered to VHE energies by the non-thermal electrons accelerated at the external forward shock. Our calculations show that the EIC flare nearly coincides with the late-prompt flare, but extends ∼ 3 − 4 times longer than the duration of the late-prompt flare. The preferred kinetic energy and initial Lorentz factor used in our model are ∼ 10 52 erg and ∼ 20, respectively. Understanding the mechanisms of the VHE emission from low-luminosity GRBs will help us constrain the properties of the outflow and the central engine activities, as well as the particle acceleration mechanism.