The aim of the present study was to estimate the wall effect of the self-made spherical graphite-walled cavity chamber with the Monte Carlo method for establishing the air-kerma primary standard of high-dose-rate (HDR) ¹⁹²Ir brachytherapy sources at the Institute of Nuclear Energy Research (INER, Taiwan). The Monte Carlo method established in this paper was also employed to respectively simulate wall correction factors of the ¹⁹²Ir air-kerma standard chambers used at the National Institute of Standards and Technology (NIST, USA) and the National Physical Laboratory (NPL, UK) for comparisons and verification. The chamber wall correction calculation results will be incorporated into INER's HDR ¹⁹²Ir primary standard in the future. For the brachytherapy treatment in the esophagus or in the bronchi, the position of the isotope may have displacement in the cavity. Thus the delivered dose would differ from the prescribed dose in the treatment plan. We also tried assessing dose distribution due to the position displacement of HDR ¹⁹²Ir brachytherapy source in a phantom with a central cavity by the Monte Carlo method. The calculated results could offer a clinical reference for the brachytherapy within the human organs with cavity.