Grain-growth kinetics of high-entropy, single-phase, face-centred cubic (FCC) Al0.2CoCrFeNi alloy was studied by isothermal annealing over a wide temperature range for different time intervals. Both optical and EBSD studies show a significant amount of annealing twins. Data were analysed using classical grain-growth models and the activation energy was estimated using the Arrhenius type equation. The grain-growth exponent was found to be n = 3 and the measured activation energy for grain growth was 190 ± 15 kJ mol−1. Significant resistance to grain growth was observed at 1100°C. Microstructural characterisation tools like EBSD, along with nanoindentation, was used to understand the observed behaviour. © 2021 Informa UK Limited, trading as Taylor & Francis Group.