High-fidelity dynamic models of solid oxide fuel cells (SOFCs) capture the spatial distribution of key performance variables by considering the cells as distributed parameter systems. As such, they are often complex and require extensive computational resources. In this paper, driven by the need to support the control strategy development and system optimization, we develop a low-order SOFC model by approximating the mass and energy balance dynamics in the fuel and air bulk flows using quasi-static relations. However, due to the coupling between the quasi-static mass balance and current distribution, this approximation leads to a large set of coupled nonlinear algebraic equations that have to be solved online using iterative computation. In order to mitigate the computational cost involved, an efficient iterative algorithm is proposed to solve these equations. The new algorithm requires to iterate on only one variable—the cell voltage—to determine the current and flow compositions and their distributions. The low-order model with 16 states is compared to the baseline model, which has 160 states that incorporates fully the mass and energy balance dynamics. Simulations are performed to evaluate the model performance for both steady-state and transient operations, and to assess the computational cost associated with the low-order and full order models. It is shown that the low-order model closely matches the original baseline model, while the computation time is reduced by more than 50% compared to the baseline model.