A hydro-carbon injection supply unit includes a fuel filter including a damping head which reduces a high fuel pulsation pressure generated in a cylinder head through an inner circulation path along of the fuel, and an HCI part for receiving the fuel discharged from the fuel filter whose pulsation pressure has been reduced and injecting the fuel to an exhaust manifold at a front end of a catalyst. Accordingly, even if a fuel pulsation pressure exceeding a design value is generated in the cylinder head, the HCI part is not influenced at all.