An exhaust device of an internal combustion engine for reducing exhaust sound and for suppressing the occurrence of a torque valley. A sound-deadening and pressure-dissipating device connected to the downstream end of an exhaust pipe includes a spherical member having an opening portion opening toward a downstream edge of the exhaust pipe. Exhaust gas from the exhaust pipe is reflected by an inner spherical surface of the spherical member to reduce exhaust pressure in the spherical member and then is discharged from the opening portion.