Numerical method is popular in analysing the blast wave propagation and interaction with structures. However, because of the extremely short duration of blast wave and energy transmission between different grids, the numerical results are sensitive to the finite element mesh size. Previous numerical simulations show that a mesh size acceptable to one blast scenario might not be proper for another case, even though the difference between the two scenarios is very small, indicating a simple numerical mesh size convergence test might not be enough to guarantee accurate numerical results. Therefore, both coarse mesh and fine mesh were used in different blast scenarios to investigate the mesh size effect on numerical results of blast wave propagation and interaction with structures. Based on the numerical results and their comparison with field test results and the design charts in TM5-1300, a numerical modification method was proposed to correct the influence of the mesh size on the simulated results. It can be easily used to improve the accuracy of the numerical results of blast wave propagation and blast loads on structures.