This work presents an improved finite-control-set model predictive flux control (FCS-MPFC) for asymmetrical six-phase permanent magnet synchronous machine (ASPMSM) with a novel duty-cycle regulation strategy. Firstly, virtual vector concept is adopted to suppress harmonic currents without additional cost function and the corresponding weighting factor. Then, 12 virtual vectors with higher voltage utilization are developed. Meanwhile, for the sake of strengthening steady-state performance, a novel duty-cycle regulation strategy incorporating the well-known Lagrange multiplier method is proposed. In this strategy, the reconfigurable set of voltage vectors (SVV), which consists of an active and a null virtual vector, can be determined without second modification, hence highly mitigating additional computation burden. Furthermore, in order to realize the purpose of unified switching frequency, the SVVs are implemented in terms of regular rather than irregular PWM signal pattern. Finally, experimental results prove the effectiveness of the proposed method.