This paper is devoted to the analysis of the effect of gas injection on the efficiency of gaseous fuel burning. A coaxial burner with a perforated inner wall is presented in which the methane–air acceleration is observed. With the use of numerical analysis, it is demonstrated that the flame acceleration is related to the flow separation from the inner wall that, in turn, leads to the reduction in heat losses to the wall as well as to vortex formation and reduction in momentum losses. On the basis of the obtained results, a new technology of efficient burning of gaseous fuels can be proposed with the use of gas and/or liquid fuel injection.