A muffler is equipped with a catalytic converter and is compact and capable of stably supporting the catalytic converter disposed in a muffler box with a single partition. The muffler box is formed by joining outer peripheral ends of three parts which are first and second box halves with open surfaces thereof abutting each other and a partition interposed between the first and second box halves. A first silencing chamber communicating with an exhaust inlet pipe is defined between the first box half and the partition and a second silencing chamber communicating with a tailpipe is defined between the second box half and the partition. A pair of supporting bosses protruding toward the first and second silencing chambers, respectively, are formed in the partition, and the supporting bosses support a holding tube of the catalytic converter communicating between the first and second silencing chambers.