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Auto-ignition of a non-homogeneous mixture was fundamentally investigated by means of a numerical calculation based on chemical kinetics and the stochastic approach. In the present study, the auto-ignition process of n-heptane is calculated by means of a reduced mechanism developed by Seiser et. al. The non-uniform states of turbulent mixing are statistically described using probability density functions and the stochastic method, which was originally developed from Curl's model. The results show that the starting points of the low-temperature oxidation and ignition delay period are hardly affected by the equivalence-ratio variation; however, combustion duration increases with increasing variance of equivalence ratio. Furthermore, combustion duration is mainly affected by the non-homogeneity at the ignition and not very much affected by the mixing rate.