Disclosed are a fuel supply module that may maintain an entrainment ratio in a constant range even under a load change, and a fuel reforming apparatus for a fuel cell using the same. The fuel supply module includes: a water vapor storage for storing water vapor therein; a fuel storage for storing fuel therein; a mixer having a first inlet, a second inlet, and an outlet; a first inlet pipe for connecting the water vapor storage and the first inlet of the mixer with each other; a second inlet pipe for connecting the fuel storage and the second inlet of the mixer with each other; an outlet pipe connected to the outlet of the mixer; and a bypass pipe having one end connected to the first inlet pipe and the other end connected to the outlet pipe.