Current study on air-leakage of compressed air energy storage (CAES) cavern is focused on the global air-leakage seepage field without consideration of the thermo-gas-mechanical (TGM) coupling theory. In this study, a new theoretical model of local air-leakage seepage field for the lined CAES cavern is established based on the thermo-gas-mechanical (TGM) coupling theory and boundary conditions of the non-continuous and non-axisymmetric seepage. Calculation results show that with the increasing of the air-leakage distance, the local air-leakage seepage field p(r,θ,t) is decreased fast at first and then tends to the stable value p(r,θ,t)= 0.1 MPa (atmospheric pressure) at the maximum leakage distance RAA'm (when the air-leakage is stopping). The distribution area of the local air-leakage seepage field (related to the radius r and polar angle θ) is increased gradually from the non-axisymmetric about the center of cavern fan-shape and peach-shape to the axisymmetric circle, which is different from that of the global air-leakage seepage field (circle, independent of θ ). The new theoretical model of local air-leakage seepage field is proved to be valid by numerical simulation results and provides a scientific basis for the safety assessment of the underground geotechnical engineering with local fluid-leakage.