The standard bi-exponential impulse voltage waveforms recommended by IEC are mainly used for the development, design and testing of oil-immersed shunt reactors, but the measured intrusion overvoltage waveforms are usually characterised by bipolar decay and oscillation. In this work, a test rig was constructed to investigate the breakdown failure characteristics of oil-paper insulation under bipolar oscillating decaying impulse voltages with different test waveform parameters. The results show that the waveform parameters have a large impact on the waveform position and insulating paper morphology during breakdown, the logistic distribution has a better fitting effect on the breakdown probability data, and the smaller the attenuation constant and the higher the oscillation frequency, the more difficult it is for the oil-impregnated insulating paper to break down. The results provide a reference for the re-development and design of reactors, as well as a basis for the assessment of the voltage intolerance performance of power equipment.