The process of oil-gas separation is an important part of oilfield surface engineering. The oil-gas separator is the key equipment in this process. The composition of produced fluid from oil well is complex and the flow state of it changes frequently, which leads to the abnormal operating condition of the separator and affects the continuity of oil production. Therefore, the operating condition diagnosis of the oil-gas separator is extremely important for the system of oil production. Compared with the traditional threshold-based alarm method, the data-driven diagnosis method is more accurate and intelligent. According to the multivariate time series properties of the data of supervisory control and data acquisition (SCADA) system, the convolution neural network (CNN) is proposed to extract the multi-dimensional features of the oil-gas separator. Then based on the extracted features, the slug flow conditions of oil-gas separator are diagnosed, whose process is visually analyzed by t-distributed stochastic neighbour embedding (t-SNE). Finally, the data-driven diagnosis method of the oil-gas separator is realized, and the simulation data show that the average fault diagnosis rate of this method reaches 97.78%, which is 26.95% higher than that of the traditional method. The method proposed can diagnose the operating conditions of the separator accurately and quickly.