A combustor (10) includes a combustion chamber (18), a liner (12) surrounding the combustion chamber, and a flow sleeve (52) surrounding the liner. An annular passage is between the liner and the flow sleeve, and a fuel injector (50) is located partially in the annular passage and extending through the liner into the combustion chamber. The fuel injector includes an outer tube, an inner tube, and a flow passage. A method of supplying a fuel to a combustor includes flowing a diluent inside an outer tube extending along a liner and flowing a liquid or gaseous fuel inside an inner tube extending inside a portion of the outer tube. The method further includes flowing the diluent and the liquid or gaseous fuel through the liner and into a combustion chamber surrounded by the liner.