Modeling and understanding of underground coal fire is of significance for green-and-safe mining of coal resources in China. Two issues remain unsolved in forward-propagation models of underground coal smoldering fires: one-step coal oxidation has been too simple so that endothermic reactions such as water evaporation and pyrolysis that have important influence on smoldering propagation of underground coal fires have been not considered; and models have not been validated via experimental data. In this work, a three-step chemical reaction scheme including water evaporation, coal pyrolysis, and char oxidation was employed and mathematic model in terms of forward propagation of underground coal smoldering fires was established. The theoretical model was numerically calculated using COMSOL Multiphysics finite element software. The theoretical model was numerically calculated using COMSOL Multiphysics finite element software, and the forward smoldering spread experiment of underground coal fire driven by thermal buoyancy under different ground crack permeability conditions was carried out. Comparison experiment and numerical calculation were carried out. Results show that the proposed model not only owns good capability to predict the peak temperature and velocity of smoldering propagation of underground coal fire, but also can inversely plot multiple step chemical reactions as well as spatiotemporal evolutions of oxygen and solid species mass fractions. In addition, the controlling mechanism of smoldering propagation of underground coal fires was further revealed.