A model of turbulent combustion and ignition of polydisperse dust-air mixtures is developed. The mathematical model allows for interactions between the gas and dust phases and combines the deterministic and stochastic approaches to their description. The equations governing particle motion include random turbulent fluctuations of the gas flow. The models of phase transitions and chemical reactions take into account thermal destruction of dust particles, sublimation of volatiles, chemical reactions in the gas phase, and heterogeneous carbon oxidation by O2 and CO2 which depends both on diffusion and kinetic parameters. The model was compared with experimental data on combustion of organic dust in closed vessels at various initial turbulence intensities. The suggested mathematical model permits the peculiarities of ignition and burning of polydisperse organic dusts and the effect of flow inhomogeneity on the ignition limits to be studied.