An exhaust device includes an exhaust pipe connected at its upstream end to a cylinder head of the engine and an exhaust muffler connected to the downstream end of the exhaust pipe for suppressing the generation of noise from a heat insulating cover that covers a part of the exhaust pipe. A heat insulating cover covers a portion of the exhaust pipe near the engine and a stay is fixed to the heat insulating cover. The stay includes a supporting plate portion curved so as to partially surround the outer circumference of the exhaust pipe. A first vibration isolating member is provided that is sandwiched between the outer circumference of the exhaust pipe and the supporting plate portion, a band member is tightened to mount the supporting plate portion to the exhaust pipe, and a second vibration isolating member is sandwiched between the supporting plate portion and the band member.