Based on the non-uniform constitution of coal, coal liquefaction is conveniently described by a mathematical model, in which the overall liquefaction is achieved in two stages. Both stages consist of a series of parallel irreversible reactions, of which the activation energies obey normal distribution. When catalysts exist in the reaction system, they can decrease the activation energies of the second stage, but have little effect on the reactions of the first stage. This model improves the understanding of why some coal constituents are easy to liquefy while others are not. It successfully predicts that apparent activation energies increase with conversion. The predicted conversion values derived from this model show good agreement with our experimental data as well as with the data reported in the literature.