To　address　the　pollution　problem　caused　by　unbalanced　nonlinear　loads　on　the　grid,　this　paper　proposes　a　modular　multilevel　converter-based　active　power　filter　(MMC-APF)　for　optimal　composite　control　of　compensation　currents　based　on　multi-step　model　prediction.　The　compound　control　of　PI　and　repetitive　control　(RC)　is　used　to　obtain　the　number　of　bridge　arm　pre-conductor　sub-modules.　On　this　basis,　the　multi-step　model　predictive　control　is　used　to　narrow　the　search　range　for　finding　the　optimal　level　of　the　objective　function.　There　is　no　need　to　design　the　weighting　factors,　and　the　total　number　of　sub-modules　put　into　per　phase　bridge　arm　is　[N−1,　N+1],　which　can　achieve　2N+1　maximum　level　number　output,　enhancing　the　MMC-APF　AC　side　current　tracking　accuracy　and　improving　the　system　dynamic　performance.　Meanwhile,　a　grouped　hierarchical　voltage　equalization　modulation　strategy　based　on　the　predicted　values　of　sub-module　capacitance　voltages　is　proposed,　reduces　the　computational　complexity　of　the　equalization　process,　and　lowers　the　switching　frequency　of　sub-modules.　Finally,　the　MMC-APF　platform　is　built　to　verify　the　effectiveness　of　the　proposed　research　scheme.　©　The　Author(s),　under　exclusive　licence　to　Springer-Verlag　GmbH　Germany,　part　of　Springer　Nature　2025.