An analysis of a solid oxide fuel cell (SOFC) working with direct internal reforming of methane when subjected to unsteady conditions is presented in this paper. A cell of planar type with the anode-supported structure and the co-flow configuration is investigated. Owing to the reforming and the water-gas shift reactions, it has been known that the steady operation of a cell working with natural gas is different from that with hydrogen. Moreover, since these chemical reactions are strongly temperature-dependent, the former is expected to become much more complex than the latter under unsteady states. It is necessary in the viewpoints of degradation and performance efficiency to understand the evolution of the thermal gradient/stress, the fuel concentration, etc. when the cell is subjected to changes such as load demand. In this work, a three-dimensional numerical model is employed and step changes of the output voltage are introduced to the cell. Results for the temporal profiles of the temperature, the current density, the activation overpotential and the gas concentration distributions in the cell are presented and discussed. It is found that the overshoot in the activation does not appear throughout the cell, but only in the exit region when the voltage jumps from 0.7 V to 0.6 V. (C) 2016 Elsevier Ltd. All rights reserved.