Solid oxide fuel cells (SOFCs) are promising power-generation systems to utilize methane or methane-based fuels with a high energy efficiency and low environmental impact. A successive multi-stage process is performed to explore the operation of cells using dry methane or the deposited carbon from methane decomposition as fuel. Stable operation can be maintained by optimizing the fuel supply and current density parameters. An electrochemical impedance analysis suggests that the partial oxidization of Ni can occur at anodes when the carbon fuel is consumed. The stability of cells operated on pure methane is investigated in three operating modes. The cell can run in a comparatively stable state with continuous power output in an intermittent methane supply mode, where the deposition and utilization of carbon is controlled by balancing the fuel supply and consumption. The increase in the polarization resistance of the cell might originate from the small amount of NiO and residual carbon at the anode, which can be removed via an oxidation-and-reduction maintenance process. Based on the above strategy, this work provides an alternative operating mode to improve the stability of direct methane SOFCs and demonstrates the feasibility of its application.