In this paper, coupled heat and mass transfer during the desorption process of a metal–hydrogen reactor (LaNi5–H2) is numerically investigated. To predict the dynamic behavior of this reactor, a new algorithm based on the lattice Boltzmann method (LBM) is proposed as a potential solver. Based on this algorithm, a computer code is developed using fortran 90. This algorithm is validated successfully by comparison with experimental data reported in the literature and results obtained by finite volume method (FVM). Using the developed code, the time–space evolutions of the temperature and the hydride density within the reactor are presented. In addition, the effect of some parameters (applied pressure, heating temperature, and overall heat transfer coefficient) on the dynamic behavior of the reactor is evaluated. Compared to the FVM, the proposed algorithm presents simple implementation on a computer and with reduced CPU time.