The dynamic characteristics of a bubble initially very close to a rigid wall, or with a very narrow gap, are different from those of a bubble away from the wall. Especially at the contraction stage, a high-speed jet pointing toward the wall will be generated and will impact the rigid surface directly, which could cause more severe damage to the structure. Based on the velocity potential theory and boundary element method (BEM), the present paper aims to overcome the numerical difficulty and simulate the bubble impact on a solid wall for the axisymmetric case. The convergence study has been undertaken to verify the developed numerical method and the computation code. Extensive experiments are conducted. Case studies are made using both experimental data and numerical results. The effects of dimensionless distance on the bubble dynamics are investigated.