Solid oxide fuel cell (SOFC) reactions with a diluted dry methane feed were studied from chemical equilibrium analysis. The rate of carbon deposition and the composition of an anode gas mixture in equilibrium were predicted as a function of current density by minimizing the total Gibbs free energy of a system with 21 chemical species, including a condensed phase for carbon deposition. The equilibrium diagram is generally explained with three overall methane reactions of decomposition, partial oxidation, and direct oxidation. A significant amount of carbon deposition is predicted from a very high equilibrium conversion rate of methane via decomposition at the open circuit, and the carbon deposition is rapidly reduced as current applies to the cell. There is a threshold current density above which no carbon deposition is observed. This threshold current value distinguishes the range of current density with clearly different equilibrium behaviors. Partial oxidation of methane is considered the major reason for the reduction of carbon deposition in the current density range below the threshold value. Direct oxidation of methane is considered dominant at current densities much higher than the threshold value. Steam reforming does not seem to be influential in the entire range of current density.