A combustor and a gas turbine including the same which can reduce a loss of pressure and enhance a cooling efficiency of a liner and transition piece are provided. The combustor may include a liner configured to define a combustion chamber, a transition piece coupled to a rear end of the liner, a flow sleeve configured to surround the liner and the transition piece, a plurality of impingement holes formed in the flow sleeve, and a plurality of inserts inserted into at least some of the impingement holes, wherein each of the inserts may include a first channel configured to guide combustion air, introduced into an associated one of the impingement holes, in a direction parallel to a direction of extension of an annular passage between the flow sleeve and the liner or an annular passage between the flow sleeve and the transition piece, and a second channel configured to guide the combustion air, introduced into the associated one of the impingement holes, in a direction transverse to the annular passage between the flow sleeve and the liner or the annular passage between the flow sleeve and the transition piece.