This paper presents a predictive control strategy for grid-connected cascaded H-bridge (CHB) converters under unbalanced power generation among each converter phase. The proposed controller belongs to the finite-control-set model predictive control (FCS-MPC) family and is designed to extract unbalanced power from each CHB converter phase while providing balanced power to the grid. The key novelty of this strategy lies in the way the unbalanced power generation among the phases is explicitly considered into the optimal control problem. Power balance is achieved by enforcing the CHB converter to work with a suitable zero-sequence voltage component. The proposed predictive controller is directly formulated in the original abc-framework to account for the common-mode voltage. Simulation and experimental results are provided to verify the effectiveness of the proposed FCS-MPC strategy.