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The rapid and accurate identification of large-scale orbital angular momentum (OAM) modes is crucial for expanding the application of vortex beams (VBs). In this paper, an OAM mode recognition method based on convolutional neural networks (CNNs) is proposed and investigated. We construct an 8-layer CNN possesses complex feature extraction capability and train it to own powerful anti-turbulence competence by feeding the intensity patterns of VBs interfered by Gaussian beam. After supervised training of a large sample set, the CNN model takes on excellent network generalization ability and can well detect VBs with the mode range of [-50,50]. The simulation results indicate that under the influence of weak and medium turbulences, the average recognition accuracy exceeds 99%. Even under strong turbulence, the accuracy also reaches 98.54%. Meanwhile, the identification time is only 1.55ms per OAM mode with Intel(R) Xeon(R) Gold 6148 CPU. Moreover, the influence of different Gaussian beam waists, VB orders, input training sets, and CNN structures on OAM mode recognition performance, is fully studied. These results demonstrate that our proposed method can achieve higher accuracy and higher order OAM mode detection at a fast speed, which contributes a more effective method for the recognition of VBs.