NOVELTY - A fuel reforming apparatus comprises a fuel decomposition unit to decompose a first hydrocarbon-based fuel into a second hydrocarbon-based fuel with a lower carbon number, and a reforming reactor having a catalyst for promoting a reforming reaction. The reactor produces a hydrogen-rich gas from the second hydrocarbon-based fuel by the reforming reaction.    USE - For producing a hydrogen-rich gas from a hydrocarbon-based fuel.    ADVANTAGE - The invention reduces formation of soot, thus preventing situations in which the surface of the reforming catalyst is covered with soot reducing the activity of the reforming reaction. It increases the efficiency of the reforming reaction in the reactor. The reforming reaction can be conducted at a lower temperature and the reforming unit can be made more compact. Decomposing the hydrocarbon-based fuel before feeding it to the reforming reactor makes it possible to prevent situations in which the activity of the reforming reaction is reduced by the adsorption of the hydrocarbon-based fuel on the catalyst surface.    DETAILED DESCRIPTION - INDEPENDENT CLAIMS are also included for;    (1) A fuel cell system comprising a fuel cell generating electromotive force by electrochemical reactions, and the above fuel reforming apparatus;    (2) A fuel reforming method for producing a hydrogen-rich gas from a hydrocarbon-based fuel comprising decomposing a first hydrocarbon compound into a second hydrocarbon-based fuel with a lower carbon number, and producing a hydrocarbon-rich gas from the second fuel by a reforming reaction; and    (3) A method for starting up a fuel cell system by raising a ratio of an amount of oxygen to that of the first hydrocarbon-based fuel fed to the fuel decomposition unit until the fuel is heated up to a specified temperature, thus causing partial oxidation of the first fuel and promoting oxidation of hydrogen and carbon monoxide produced by the partial oxidation on an anode-side catalyst inside the fuel cell.    DESCRIPTION OF DRAWING(S) - The figure shows a block diagram of the fuel cell system.