The Partial breakdown (PBD) and complete breakdown (BD) voltage characteristics in a composite insulation system of glass fiber reinforced plastics (GFRP) and liquid nitrogen are investigated to find the PBB and BD characteristics in solenoid type high temperature superconducting (HTS) coils at quench. The electrode system used is made from a coaxial spiral coil-to-cylindrical electrode with an insulation barrier and spacers, and is immersed in liquid nitrogen. A heater is mounted inside the coil electrode to generate boiling which occurs on quenched superconducting coils. The experimental results show that: (1) breakdown voltages are affected severely by the risetime of the applied voltage and the PBD inception voltage, (2) two kinds of BD mechanisms are found depending on the shape of the spacer, length of cooling channel and heater power.