Numerical oscillation can easily be found in dealing with the thermoacoustic convection problems for its steep gradient in consideration of which flux-correct transport algorithm (FCT) and timestep splitting technique was considered.FCT combining with timestep splitting techniques method had been presented to simulate the steep gradient thermoacoustic convection problems which was caused by impulse heating.The simulated results had a nice agreement with the experiment .These analysis and comparisons indicated that this method completely can be used for simulating thermoacoustic convection.