A combustor has an axial fuel staging system to allow a fuel-air mixture to be injected from two axially spaced stages using an injector for injection of a secondary fuel-air mixture. The combustor includes a liner defining a combustion chamber; a transition piece coupled to a rear end of the liner; a flow sleeve defining an annular channel by surrounding the liner and the transition piece; and at least one injector disposed on a circumferential position of the flow sleeve to inject a mixture of fuel and air into the combustion chamber. Each of the at least one injector includes an injection pipe extending radially and passing through both the flow sleeve and either of the liner and the transition piece; a plate coupled to the injection pipe; and a plurality of mixing passages formed through the plate. The combustor improves fuel-air mixing and prevents flash back.