To provide a support structure of an exhaust pipe of a vehicle whose vibration is suppressed to reduce influence upon the inside of a cabin.

In an engine 1 transversely installed in a vehicle front part, a power plant side mount bracket 12 of a rear engine mount 5 is installed with a hanger rubber 13, and the hanger rubber 13 is installed with a hanger pipe 15 fixed to the exhaust pipe 8. Because the exhaust pipe 8 is installed to the mount bracket 12 through the hanger rubber 13, a vibration isolation structure is reduplicated to the exhaust pipe 8. Accordingly, the vibration transmitted to a vehicle body from the exhaust pipe 8 is damped to reduce a noise into the cabin. Because installation work of the exhaust pipe 8 requires only engagement of the rear engine mount 5 with the mount bracket 12, installability is improved.