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To study the current response to space charge in oil–paper insulation, a simultaneous space charge and external current measurement system are developed for a solid–liquid sample. The space charge and external current of oil-immersed paper are tested under different applied voltages. In the oil–paper sample, it accumulates heterocharge at 0.25 kV and homocharge at a higher voltage. The external currents first decrease and then increase with time. The changing timepoint decreases with the applied voltage. It shows that dynamic space charge evolution influences external current development. An unusual phenomenon is observed that the charge on both electrodes increases without heterocharge accumulation in a certain time range after voltage application, resulting in an increase in the average electric field. The transient electric field and displacement current at the cathode are calculated according to the amount of surface charge at the cathode. It indicates that displacement current takes up the main part of external current and decreases to zero when the surface charge amount stops increasing. After this stage, the conduction current is almost equal to the external current. The correlation between conduction current and electric field is analyzed. It reveals that when the electric field is lower than 5 kV/mm, the conduction current of oil–paper seems to be linear to the electric field strength, following Ohm’s law. When the electric field is higher than 5 kV/mm, the conduction current of oil–paper follows the Fowler–Nordheim law that the ln(jc/E2) is linear to 1/E. The transient external current has great potential in diagnosing electrical equipment.