In the dielectric insulation design of any high temperature superconducting (HTS) apparatus as well as HTS fault current limiter in the electrical power systems, the breakdown characteristics of cryogenic coolants such as liquid nitrogen ($LN_2$) are an important factor of the insulating engineering. Previous reports concerned with the breakdown characteristics of liquid nitrogen have pointed out that bubbles and gaseous nitrogen have a treat influence on their breakdown phenomena, However, useful data for practical insulation design of HTS fault CUITent limiter operating at subcooled L$N_2$ have not been obtained enough. Therefore, this paper presents an experimental investigate of breakdown phenomena in liquid nitrogen under AC voltage, And, we observed the breakdown voltage (BDV) of liquid nitrogen with lowering temperature. The Weibull plots of the breakdown voltage of subcooled $LN_2$ for the needle-plane electrode with d= 10 mm are studied, The dependence of breakdown voltage for needle-plane and pancake coil-pancake coil electrode on temperature is illustrated, The relationship between the AC breakdown characteristics and the temperature were clarified.