This　article　proposes　a　generalization　of　the　model-free　predictive　current　controller　(MFPCC)　for　multilevel　voltage　source　inverters　(VSIs).　MFPCC　is　an　alternative　to　mitigate　the　parameter　sensitivity　faced　by　model-based　PCC　(MPCC),　but　it　requires　a　constant　update　of　the　stored　current　variations　(CVs)　associated　with　each　VSI　state　to　provide　a　prediction,　which　results　in　a　satisfactory　closed-loop　response.　When　a　multilevel　VSI　is　considered　the　number　of　states　increases,　which　results　in　a　decrease　of　the　CV　update　rate,　since　only　one　state　can　be　updated　at　each　sample.　To　solve　this　issue,　the　extended　adjacent　state　scheme　is　used　to　reduce　the　possible　number　of　solution　candidates　and　then　a　controlled　CV　is　used　to　compensate　the　updated　CV.　Simulation　and　experimental　results　obtained　with　a　sampling　rate　of　5　kHz　show　that　the　proposed　MFPCC　exhibits　performance　similar　to　the　one　of　MPCC　for　nominal　parameters.　However,　a　better　current　response　is　obtained　in　the　case　of　the　load　parameter　mismatch,　especially　at　steady　state.