The finite control set model predictive control (FCS-MPC) for power electronic converters provides high dynamic performance, based on the limited number of inputs and accurate model of the converter. By applying this algorithm to multilevel converters such as a cascaded-H-bridge-based static var compensator (CHB STATCOM), the dynamic performance is degraded, because the optimized input is achieved by searching among a large set of switching combinations and redundancies. This paper proposes an FCS-MPC algorithm, which benefits high dynamic performance for the CHB STATCOM, despite the large set of inputs. The proposed FCS-MPC replaces the time-consuming optimization algorithm by solving Diophantine equations over the large set of switching combinations. The desired switching combination and all its redundancies are determined in a minimum execution time. The proposed FCS-MPC performance is validated by applying to two configurations: 1) a 15-level CHB STATCOM with energy storage capability for a short-term active power smoothing and reactive power compensation of a 10 MW fixed speed wind farm at medium voltage; and 2) an experimental seven-level CHB STATCOM at low voltage.