A dual fuel system for an engine is disclosed. The dual fuel system may have a first fuel supply providing a first fuel to the engine, and a second fuel supply providing a second fuel. The dual fuel system may also have a regulator configured to pass the second fuel from the second fuel supply to the engine, with the regulator also in fluid communication with the first fuel supply. The dual fuel system may further have a damper in fluid communication with the first fuel supply and an output of the regulator.