The invention relates to a test method and device of the magnetization characteristic of a magnetic core under a fast pulse voltage. By adopting the primary pulse voltage gradient, i.e., Vp/(n.Se.tr) of a unit area single-turn feed-in induction cavity as a characteristic parameter for representing the magnetization field intensity characteristic of the magnetic core and by changing the charging voltage or the winding turn of a fast front edge pulse voltage generator, the hysteresis loop of the magnetic core under the fast pulse voltage with different characteristic parameters can be acquired through testing. The test device disclosed by the invention comprises a low-induction capacitor C, a fast pulse resistance voltage divider RD1/RD2, a short-gap gas switch Gap, a primary winding, a secondary winding, a current coil and an outer cylinder. The test device can generate a fast front edge pulse voltage with the front edge being less than 20ns and the amplitude being 20-80kV and reaches the magnetization field intensity characteristic parameter value under actual working conditions of an FLTD (Fast Linear Transformer Driver) and an IVA (Ideal Voltage Amplifier).