Classification of lightning produced VLF/LF signals plays crucial role in the detection and location of lightning flashes. The machine learning method has potential in the VLF/LF lightning signal classification. Traditional machine learning methods are data-driven and work in a black-box fashion, making the classification accuracy highly dependent on the size and quality of dataset. In this paper, an interpretable convolutional neural network model is proposed for VLF/LF lightning electric field waveform classification. Multi-scale convolutional kernels and shortcut connections are adopted in this model to enhance the ability to capture local waveform features. The CAM method is embedded in our model to open the black-box by visualizing the weight of different waveform features on the classification results. Based on the measured data from five different provinces in China, an accuracy of 98.5% is achieved in a four-type classification task including RS, active stage of IC, PB and NB. The correlation between the weight values of different waveform features and corresponding lightning discharge process are analyzed. It is found that the proposed model can extract decisive features of VLF/LF lightning signals closely related to the physical process of lightning discharges, which is similar to the human expert’s behavior. The proposed model is validated by using an open-source dataset from Argentina. It is indicated that the proposed model can resist the impact of unexpected waveform oscillation and achieve a higher accuracy of 98.39% than that of the support vector method. It is demonstrated that our model is less dependent on the training dataset.