The numerical modeling of the combustion of air-dried Victorian brown coal in O-2/N-2 and O-2/CO2 mixtures with 21-30% O-2 has been conducted via the use of computational fluid dynamics (CFD), ANSYS FLUENT 13.0, with the refined weighted-sum-of-gray-gases model (WSGGM), the single-film model with multiple surface reactions (i.e., char-O-2, char-CO2, and char-H2O) for char particle, and the refined two-step mechanism for the oxy-firing of methane to mimic the volatile oxidation. The purpose of this study is to verify the experimental observations in a lab-scale drop-tube furnace (DTF) and to promote the understanding on the details underpinning the combustion characteristics of Victorian brown coal, the youngest coal in the world and the single largest source for power generation in Victoria, Australia. As confirmed, the modeling results show good agreement with the experimental measurements on the particle temperature, coal ignition delay photographed by a high-speed camera, carbon burnout rate, and particle velocity. The air dried Victorian brown coal bears an extremely high reactivity for devolatilization and char-O-2 and char-CO2 reactions. The inherent moisture in coal was released with volatile matter simultaneously rather than as that predicted by the CFD wet combustion module for pulverized coal with surface moisture. Increasing the secondary gas temperatures greatly narrowed coal ignition delay caused by the substitution of 21 % O-2 balanced in CO2 for air. At the furnace temperatures of 1073 and 1273 K, the contribution of char-CO2 to coal burnout reached approximately 10 and 25% in the oxy-fuel mode, respectively, which, in turn, reduced the coal particle temperature by a maximum of 300 K. To achieve an identical flue gas temperature with the aid-firing case, the use of 30% O-2 in CO2 is essential. However, the radiation heat flux match can be achieved by the substitution of 27% O-2 in CO2 for air.