The combustion characteristics of the advanced vortex combustor (AVC) burning H2 fuel are studied numerically. First, using the 19-step reaction mechanism, the flame morphology of the pre-mixed H2/Air combustion under the different conditions, is computed. The calculation results are in agreement with experimental data from the literature. Second, a numerical model of a lean premixed H2/Air combustion is set up, based on the 19-step reaction mechanism. A numerical simulation is carried out to study the combustion characteristics of the AVC. The results show that the combustion can be steadily maintained, with the equivalence ratio of the H2/Air main flow kept at 0.45. At the same time, the total pressure loss coefficient is 2.77% and the combustion efficiency is 99.8%. The total pressure loss, vortex configuration and stability, combustion efficiency of the AVC are influenced by the equivalence ratio, total pressure and static pressure of main flow in the AVC.