As a new energy technology with distributed generation prospects, the load-following capability of solid oxide fuel cell (SOFC) systems is one of the main obstacles for commercial operation. This paper introduces a time delay control with an observer (1TDO) in the fuel supply system to enhance the load-following capability to realize rapid load-following without fuel starvation. A dynamic model reflecting a 5-kW SOFC system with components such as a cell stack, combustor, heat exchanger and gas supply is developed in MATLAB/Simulink to implement time delay control. TDO is improved to TDOF (time delay control with an observer and filter) to avoid the undesirable impact of external disturbances (such as fuel disturbances) on the stability of the SOFC system. The fuel supply system can be driven by the TDOF controller to closely follow the reference trajectory based on the past responses and the input variables of the system during load-following operation. Simulation results reveal that the SOFC system is able to meet the requirement of load-following due to the satisfactory dynamic performance when the TDOF controller is applied in the fuel supply system. The system is appropriate for complicated power environments. (C) 2016 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.