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A grid-forming inverter (GFI) plays an important role in providing voltage and frequency support for island microgrids. This paper proposes a computationally efficient finite-set model predictive voltage control (EFS-MPVC) scheme for GFIs. To eliminate the state prediction process, a hybrid voltage-vector reference is first synthesized using the deadbeat principle, which enhances the steady-state performance and robustness to model mismatches. Then, a voltage-vector-based cost function is designed, and a fast optimal-voltage-vector (OVV) selection scheme is built to avoid multiple enumerations. Further, to reduce the additional computing efforts caused by current constraints, an offline lookup table for fast search of OVV is established. Experimental results verify that the proposed EFS-MPVC features reduced computational amount and improved control performance in comparison to conventional MPVC schemes.