This paper presents a novel two-dimensional real-time modeling approach for a proton exchange membrane fuel cell (PEMFC) based on a tridiagonal matrix algorithm (Thomas algorithm). The Thomas algorithm consists of a forward elimination and a backward substitution, its arithmetic complexity of computations being much lower than the Gaussian elimination. In order to use this advanced numerical solver, the differential equations of reactant gas convection and diffusion phenomena in serpentine channels are transformed into a tridiagonal equations system. In addition, a three-level bisection algorithm has been developed to solve spatial physical quantities distribution for electrochemical domain. The real-time computing methods developed in this paper are then implemented in C language for a fast execution time in a real-time processor. The proposed real-time model is experimentally validated using a 1.2 kW Ballard NEXA fuel cell system, and its practical feasibilities in advanced real-time control for PEMFC systems have been experimentally demonstrated in an RT-LAB real-time simulator.