Abstract: For the establishment of γ ray air kerma primary standard in ¹³⁷Cs and making it achieve the international equivalent, a direct comparison for ¹³⁷Cs air kerma was carried out in the ¹³⁷Cs radiation field of Bureau International des Poids et Mesures (BIPM) between the National Institute of Metrology (NIM) and BIPM by using a graphite cavity ionization chamber. The comparison result is 0.996 7 with a combined standard uncertainty of 0.21%. And an indirect comparison was also made using the same chamber calibrated by NIM and BIPM, the result is 0.996 4 with a combined standard uncertainty of 0.29%. The indirect comparison result is in good agreement with the direct comparison result and the relative error is about 3×10^-4. The results have been presented in BIPM key comparison database finally.