A condensed water discharge apparatus is capable of smoothly excreting residual condensed water in a muffler. The device may include a through hole formed at the bottom of a muffler case, an inflow pipe communicated to the muffler case and in which exhaust gas flows, an exhaust pipe communicated to the atmosphere so that exhaust gas is exhausted from the muffler case thereto, a thermoelement, and a control valve mounted at the through hole so as to selectively open/close the through hole when driving or stopped by sliding about the through hole.