A liner cooling structure of a duct assembly reduces pressure loss generated in the compressed air flow for cooling the liner. The duct assembly includes a liner, a transition piece, and a flow sleeve, and the transition piece and the flow sleeve form a transition piece channel through which a main stream of compressed air is introduced to the duct assembly. The liner cooling structure includes a first flow passage through which the main stream of compressed air passes in a first direction; and a second flow passage formed as a plurality of inlet holes in the flow sleeve to communicate with the first flow passage and configured to pass an auxiliary stream of compressed air in a second direction from outside the flow sleeve to inside the flow sleeve, the auxiliary stream joining the main stream such that the second direction forms an acute angle with the first direction.