An engine-driven working machine capable of favorably reducing exhaust sound (that is, noise) is provided. An engine-driven working machine 10 is a generator in which an engine 15 and a muffler 67 are housed in an inside 13 of an outer case 12. The generator 10 includes a tail pipe 68 that is provided at a lower portion 67a of the muffler 67, a discharge port 37 that is disposed above the tail pipe 68, and a baffle plate 84 that is disposed to face the discharge port 37. The discharge port 37 is formed in the outer case 12. Further, cooling air that is sent from a cooling fan 17 is guided to below the muffler 67 with the baffle plate 84.