At present, more than 90% of China’s oil production equipment comprises rod pump production systems. Indicator diagram analysis of the pumping unit is not only an effective method for monitoring the current working condition of a rod pump production system but also the main way to prevent, detect, and rectify various faults in the oil production process. However, the identification of the pumping unit indicator diagram mainly involves manual effort, and the identification accuracy depends on the experience of the monitoring personnel. Automatic and accurate identification and classification of the pumping unit indicator diagram using new computer technology has long been the research focus of studies for monitoring the pumping unit working condition. In this paper, the indicator diagram is briefly introduced, and the AlexNet model is presented to distinguish the indicator diagram of abnormal wells. The influence of the step size, convolution kernel size, and batch normalization (BN) layer on the accuracy of the model is analyzed. Finally, the AlexNet model is improved. The improved model reduces the calculation cost and parameters, accelerates the convergence, and improves the accuracy and speed of the calculation. In the experimental analysis of abnormal well diagnosis, the data are preprocessed via data deduplication, binary filling, random line distortion, random scaling and stretching, and random vertical horizontal displacement. In addition, the image is expanded by transforming several well indicator diagrams. Finally, data sets of 10 types of indicator diagrams are created for better adaptability and application in the analysis and classification of indicator diagrams, and the ideal application effect is achieved in actual working conditions. In summary, this technology not only improves the recognition accuracy but also saves manpower. Thus, it has good application prospects in the field of oil production.