Achieving complete oxidation, good humidity tolerance and low energy cost is the key issue that needs to be addressed in plasma catalytic volatile organic compounds removal from air. For this purpose, Ag/HZSM-5 catalyst-packed dielectric barrier discharge using a cycled system composed of a storage stage and a discharge stage was studied. For dilute benzene removal from simulated air, Ag/HZSM-5 catalysts exhibit not only preferential adsorption of benzene in humid air at the storage stage but also almost complete oxidation of adsorbed benzene at the discharge stage. Five 'storage–discharge' cycles were examined, which suggests that Ag/HZSM-5 catalysts are very stable during the cycled 'storage–discharge' (CSD) plasma catalytic process. High oxidation rate of absorbed benzene as well as low energy cost can be achieved at a moderate discharge power. In an example of the CSD plasma catalytic remedy of simulated air containing 4.7 ppm benzene with 50% RH and 600 ml min⁻¹ flow rate, the energy cost was as low as 3.7 × 10⁻³ kWh m⁻³ air. This extremely low energy cost to remove low-concentration pollutants from air undoubtedly makes the environmental applications of the plasma catalytic technique practical.