A new subgrid-scale parameterization is developed to incorporate the effects of wild fires into a numerical model of the atmosphere. The parameterization is written in terms of the temperature of the combusting material and the concentration of the unburned airborne fuel. There are two central assumptions on which the parameterization rests. First, the transport of oxygen into the region of combustion, which limits the rate of oxidation, is represented by Rayleigh mixing with a fixed timescale. Second, the combusting gases and the atmosphere are treated as separate fluids. For simplicity, the effects of conduction between the combusting fluid and the atmosphere are purposely not considered in this paper. This means that the grid-scale buoyancy is defined as a volume average of the buoyancy of the combusting fluid and the ambient atmosphere, and that fire-induced buoyancy is confined to the region containing the combusting gases. These assumptions lead to a highly simplified system capturing the essence of the combustion process. The parameterization is used in a simulation of an observed grass fire in the Northern Territory (Australia).