The present paper develops a one-dimensional model of a novel coal based iron ore direct reduction process. In this process, a mixture of iron ore, coal fines and small amount of binder is made into pellets and these are placed in a bed. Air is forced upward through the pellet bed and provides oxygen for the volatiles and part of the coal in the pellets to be burnt. Initially the pellet bed is heated from the top. As the temperature of the top level of pellets increases, they start to evolve pyrolytic matter which is ignited and, as a consequence, the pellets at lower levels in the bed are heated. In this way, a flame propagates downward through the bed. The iron ore reacts with the gases evolved from the coal (including volatiles) and carbon in the coal and undergoes reduction. The model presented in the article simulates the processes occurring in the solid and gaseous phases. In the solid phase, it uses a novel porous medium model consisting of porous pellets in a porous bed with two associated porosities. The model includes equations for energy balance, reactions of iron oxide with carbon monoxide and hydrogen, coal pyrolysis and reactions between the gas components in the voids. The model shows that a rapidly increasing temperature front can travel downward through the bed if the air is supplied for long enough. The predictions of the modelling are discussed and compared with observations obtained from an experimental rig.