This thesis describes a modified advanced vortex combustor that is designed to overcome the incomplete combustion of fuel. The proposed advanced vortex combustor is characterized by a variable cross-section with a bevel and guide vanes. Detailed transient numerical simulations demonstrate the combustion characteristics of the proposed modified advanced vortex combustor. In addition, the effects of the geometry of the proposed variable cross-section on the performance of the modified advanced vortex combustor are analyzed. The results show that the proposed advanced vortex combustor achieves better flame stability and more complete combustion. Through computational analyses, it is also shown that the length of the undercut has less effects on the flow and temperature field, but too large size should be avoided taking account that the pressure loss would be increasing significantly if the flow channel is reduced.