Real-time simulation is important for the fuel cell online diagnostics and hardware-in-the-loop (HIL) tests before industrial applications. However, it is hard to implement real-time multi-dimensional, multi-physical fuel cell models due to the model numerical stiffness issues. In this paper, the numerical stiffness of a tubular solid oxide fuel cell (SOFC) real-time model is first analyzed to identify the perturbation ranges related to the fuel cell electrochemical, fluidic and thermal domains. Some of the commonly used ordinary differential equation (ODE) solvers are then tested for the real-time simulation purpose. At last, a novel two-stage third-order parallel stiff ODE solver is proposed to improve the stability and reduce the multi-dimensional real-time fuel cell model execution time. To verify the proposed model and the ODE solver, real-time simulation experiments are carried out in a common embedded real-time platform. The experimental results show that the execution speed satisfies the requirement of real-time simulation. The solver stability under strong stiffness and the high model accuracy are also validated. The proposed real-time fuel cell model and the stiff ODE solver can also help to design the online diagnostic control method.