Disclosed is an exhaust gas supply pipe for an EGR cooler of a vehicle, and more particularly, to an exhaust gas supply pipe for an EGR cooler of a vehicle, which is capable of improving an initial mounted state through a bellows and also of preventing damage caused by high exhaust heat. To this end, the present invention provides an exhaust gas supply pipe for an EGR cooler of a vehicle, including: a left pipe connected to an exhaust manifold of an engine; a right pipe connected to an EGR cooler; a bellows connecting the left pipe and the right pipe to each other and disposed at an outer periphery of the left pipe; and a heat blocking material filled in a space between the outer periphery of the left pipe and an inner periphery of the bellows.