A muffler structure capable of suppressing generation of abnormal noise in the muffler even when the outer and the inner tubes expand thermally. Provided is a double-pipe muffler structure including an inner tube and an outer tube. In the muffler structure, an annular front step portion and an annular rear step portion are formed in the inner tube, while the step portions is brought into contact, from inside, with the outer tube and thus are supported by the outer tube. The outer tube supports the front and the rear step portions by being brought into close contact with the step portions partially and elastically.