Minimum miscibility pressure (MMP) is one of the most important design parameters in CO2 flooding. Recent experimental studies show that asphaltene precipitation in light oils increases the MMP between injection gas and crude oil. To model the asphaltene-precipitation effect on MMP calculations, we develop a three-phase multiple-mixing-cell (MMC) algorithm by considering three-phase vapor-liquid-asphaltene (VLS) equilibria. This algorithm is developed by modifying the MMC method proposed by Ahmadi and Johns (Soc. Pet. Eng. J. 2011, 16, 4, 733). The three-phase VLS equilibrium calculation algorithm developed by Li and Li (Ind. Eng. Chem. Res. 2019, in press) is integrated into the two-phase MMC algorithm. Several example calculations are carried out to demonstrate the performance of our algorithm. The MMPs predicted by our algorithm and those predicted by the two-phase MMC algorithm are both compared with the MMPs measured by experiments. Comparison results show that MMPs predicted by our algorithm have a slightly better agreement with the experimental results than those predicted by the two-phase MMC algorithm.