Electromagnetic wave simulation is of pivotal importance in the design and implementation of photonic nano-structures. In this study, we developed a lattice Boltzmann model with a single extended force term (LBM-SEF) to simulate the propagation of electromagnetic waves in dispersive media. By reconstructing the solution of the macroscopic Maxwell equations using the lattice Boltzmann equation, the final form only involves an equilibrium term and a non-equilibrium force term. The two terms are evaluated using the macroscopic electromagnetic variables and the dispersive effect, respectively. The LBM-SEF scheme is capable of directly tracking the evolution of macroscopic electromagnetic variables, leading to lower virtual memory requirement and facilitating the implementation of physical boundary conditions. The mathematical consistency of the LBM-SEF with the Maxwell equations was validated by using the Champman-Enskog expansion; while three practical models were used to benchmark the numerical accuracy, stability, and flexibility of the proposed method.