CO2 flooding is an effective enhanced oil recovery process for light oil reservoirs. Asphaltenes can easily precipitate during CO2 flooding, leading to the appearance of three-phase vapor-liquid-asphaltene (VLS) equilibria. A prerequisite for accurately simulating the CO2 flooding process is developing a robust three-phase VLS equilibrium calculation algorithm. In this study, we develop a robust and efficient three-phase VLS equilibrium calculation algorithm with the use of asphaltene precipitation model proposed by Nghiem et al. [Efficient Modelling of Asphaltene Precipitation, SPE, 1993]. To develop this algorithm, a two-phase flash calculation algorithm is first developed to split the mixture into an asphaltene phase and a nonasphaltene phase. Moreover, two different three-phase VLS flash calculation algorithms are developed and incorporated into our three-phase equilibrium calculation algorithm. New initialization approaches for both stability test and flash calculations are proposed. The performance of this three-phase VLS equilibrium calculation algorithm is tested by generating pressure-composition (P-X) diagrams for several reservoir fluids mixed with pure or impure CO2.