The　conventional　model　predictive　control　(MPC)　method　of　the　non-isolated　two-stage　AC–DC–DC　converter　has　poor　robustness　and　dynamic　characteristics　under　conditions　of　model　mismatch,　external　disturbance,　and　load　disturbance.　To　solve　this　problem,　a　model-free　predictive　control　method　of　the　converter　based　on　linear　extended　state　observer　(LESO)　is　proposed　in　this　article.　First,　the　ultra-local　model　of　the　two-stage　converter　is　constructed　to　replace　the　mathematical　model.　Second,　to　improve　the　accuracy　of　the　ultra-local　model,　LESOs　are　designed　to　estimate　the　uncertain　part　of　each　control　loop.　Third,　the　cost　functions　are　adopted　based　on　the　deadbeat　control　method　to　achieve　better　dynamic　performance.　Finally,　to　further　reduce　the　output　current　ripple,　the　carrier　phase-shifting　pulse　width　modulation　is　applied.　The　experimental　results　verify　the　high　robustness　and　better　control　performance　of　the　proposed　method　in　a　two-stage　converter　compared　with　the　conventional　MPC　method.　©　2022　John　Wiley　&　Sons　Ltd.