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Cervical cancer is the seventh most common cancer among all the cancers worldwide and the fourth most common cancer among women. Cervical cytopathology image classification is an important method to diagnose cervical cancer. Manual screening of cytopathology images is time-consuming and error-prone. The emergence of the automatic computer-aided diagnosis system solves this problem. This paper proposes a framework called CVM-Cervix based on deep learning to perform cervical cell classification tasks. It can analyze pap slides quickly and accurately. CVM-Cervix first proposes a Convolutional Neural Network module and a Visual Transformer module for local and global feature extraction respectively, then a Multilayer Perceptron module is designed to fuse the local and global features for the final classification. Experimental results show the effectiveness and potential of the proposed CVM-Cervix in the field of cervical Pap smear image classification. In addition, according to the practical needs of clinical work, we perform a lightweight post-processing to compress the model.