A　multiobjective　model-free　predictive　control　(MO-MFPC)　strategy　is　proposed　in　this　article　for　multilevel　cascaded　H-bridge　(MLCHB)　inverters　with　unbalanced　conditions.　The　compensated　current　variation　(CCV),　which　allows　the　inclusion　of　the　proportional　and　integral　terms　into　the　cost　function,　is　generalized　to　improve　the　accuracy　of　MFPC　over　a　wide　range　of　applications.　The　new　extended　CCV　is　used　to　define　the　voltage　control　objective　without　involving　the　output　voltage　model　of　MLCHB.　This　voltage　control　objective　is　used　to　evaluate　all　state　candidates　to　achieve　a　suitable　subset　for　the　current　control　objective.　To　achieve　a　better　tradeoff　between　the　current　accuracy　and　the　injected　common-mode　voltage　(CMV),　CMV　is　added　to　the　cost　function.　Simulations　and　experimental　evaluations　show　that,　compared　to　existing　MFPCs　and　classic　model　predictive　control　for　MLCHB　inverters,　MO-MFPC　achieves　a　better　current　accuracy　over　a　wide　range　of　applications　and　unbalanced　MLCHB　operating　conditions.