Abstract: In order to solve the problem in direct numerical simulation based on Navier-Stokes equations to describe flame acceleration and deflagration to detonation transition of combustible gas, a Krylov implicit integration factor (IIF) method was proposed to overcome the difficulty due to the different time scale caused by the non-stiff advection-diffusion terms and stiff reaction terms in Navier-Stokes equations. Explicit scheme was used to discretize the non-stiff terms and implicit scheme to discretize the stiff reaction terms. The equations with implicit scheme make large time step size computations possible. And the large sparse matrix is projected to the Krylov subspace, and the dimension of the Krylov subspace is much smaller than the dimension of the large sparse matrix at lower computational cost. The results of numerical simulation are identical with experimental results. The results show that IIF method could apply in the simulation for NS equations well.