This paper presents a comprehensive model for the transient high-pressure vaporization process of droplets of complex liquid mixtures with large number of components in which the mixture composition, the mixture properties, and the vapor-liquid equilibrium (VLE) are described by using the theory of continuous thermodynamics. Transport equations, which are general for the moments and independent of the distribution functions, are derived for the semicontinuous systems of both gas and liquid phases. A general treatment of the VLE is conducted which can be applied with any cubic equation of state (EOS). Relations for the properties of the continuous species are formulated. The model was further applied to calculate the sub- and super-critical vaporization processes of droplets of a representative petroleum fuel mixture - diesel fuel. The results show that the liquid mixture droplet exhibits an intrinsic transient vaporization behavior regardless of whether the pressure is sub- or super-critical. The regression rate of the liquid mixture droplet is reduced significantly during the late vaporization period. The comparison with the results of a single-component substitute fuel case emphasizes the importance of considering the multi-component nature of practical mixture fuel and the critical vaporization effects in practical applications. This paper provides a practical means for more realistically describing the high-pressure vaporization processes of practical fuels,