The time-domain airborne electromagnetic (AEM) system can do fast electromagnetic (EM) surveys over mountainous areas by carrying its detection equipment on an airplane. Due to the dense sampling of the AEM method, it generates a huge amount of data. As a result, resistivity imaging methods have become the first choice for data interpretation because they are fast. However, the traditional imaging methods do not fully consider the influence of the transmitting waveform. When they are used to deal with the AEM data with complex current waveform, the imaging results are seriously affected. Therefore, we develop a universal full-field apparent resistivity imaging method for AEM data with arbitrary transmitting waveform. Firstly, we calculate the convolution of the time derivative of the current waveform and step response to obtain the time-domain AEM response of the arbitrary transmitting waveform. Then the full-field apparent resistivity imaging method based on the inverse function theorem is used to complete the rapid imaging of AEM data with complex waveform. Finally, we apply our imaging code to both synthetic and field data to verify its correctness.