We present a finite difference method for solving the equations of combustion in the limit of zero Mach number. In this limit, acoustic waves are weak and do not contribute significantly to the fluid dynamics or energetics. For the equations describing this limit, we construct an efficient. high-resolution numerical method that allows for large temperature and density variations and correctly acCOl.ll1ts for expansion due to heat release.The method, a projection method, is a second order fractional step scheme. In the first step, we compute the solution to advection-reaction-diffusion equations for the velocity, temperature, and species. In the second step, we impose the constraint on the divergence of the velocity field that represents the effect of bulk compression and expansion of the fluid due to heat release. We demonstrate our method on the problem of combustion in an enclosed container.