Tuberculosis is still one of the top 10 causes of deaths worldwide, especially with the emergence of multidrug-resistant tuberculosis. Rifampicin, as the most effective first-line antituberculosis drug, also develops resistance due to the mutation on Mycobacterium tuberculosis (Mtb) RNA polymerase. Among these mutations, three mutations at position 451 (H451D, H451Y, H451R) are associated with high-level resistance to rifampicin. However, the resistance mechanism of Mtb to rifampicin is still unclear. In this work, to explore the resistance mechanism of Mtb to rifampicin due to H451D/Y/R mutations, we combined the molecular dynamics simulation, molecular mechanics generalized-Born surface area calculation, dynamic network analysis, and residue interactions network analysis to compare the interaction change of rifampicin with wild-type RNA polymerase and three mutants. The results of molecular mechanics generalized-Born surface area calculations indicate that the binding free energy of rifampicin with three mutants decreases. In addition, the dynamic network analysis and residue interaction network analysis show that when H451 was mutated, the interactions of residue 451 with its adjacent residues such as Q438, F439, M440, D441, and S447 disappeared or weakened, increasing the flexibility of binding pocket. At the same time, the disappearance of hydrogen bonds between R613 and rifampicin caused by the flipping of R613 is another important reason for the reduction of binding ability of rifampicin in H451D/Y mutants. In H451R mutant, the mutation causes the binding pocket change too much so that the position of rifampicin has a large movement in the binding pocket. In this study, the resistance mechanism of rifampicin at the atomic level is proposed. The proposed drug-resistance mechanism will provide the valuable guidance for the design of antituberculosis drugs.