Atmospheric-pressure plasma discharge can vary with conditions, such as working gas or discharge type, and the resulting discharge current has quite different electrical features. Hence, the provision of real-time and cost-effective monitoring of atmospheric-pressure plasma discharge is possible via current classification with a deep learning model. In addition, the current generated by an atmospheric-pressure plasma jet (APPJ) can be easily obtained, so it is suitable to use a data-driven convolutional neural network (CNN) to extract and analyze the current characteristics. This study presents two CNN classification applications of the current generated by an APPJ. First, we used the time-series classification approach known as InceptionTime to predict the APPJ working gas from helium, argon, and nitrogen. Second, InceptionTime was also used to predict the APPJ discharge type as Townsend discharge or glow discharge. InceptionTime leveraged the use of the inception module to reduce dimensions and avoid overfitting. Moreover, the use of four different sizes of filters along with the maxpooling layer provided sufficient receptive fields to analyze the entire current signal. We achieved 100% accuracy on a testing set of 1125 current signals, which did not include the training data during the working gas prediction; we also achieved 86.3% accuracy on a testing set of 750 current signals, which did not include the training data during the discharge type prediction. This study proves that the CNN can extract features from the discharge current waveforms and successfully predict the discharge type and working gas of an APPJ. The high-speed computing characteristics of deep learning may also facilitate real-time monitoring or diagnosis of APPJ.