Cytopathology image analysis gives an important indication of the cervical carcinoma. Automation-assisted diagnosis has received more and more attention because of its high efficiency. Thanks to the development of artificial intelligence, supervised deep learning methods have shown promising results for cervical cell detection task. However, large amounts of labeled data are quite expensive and time-consuming for acquisition. In this paper, we propose a Classification and Localization Consistency Regularized Student-Teacher Network (CLCR-STNet) with online pseudo label mining to leverage both labeled and unlabeled data for semi-supervised cervical cell detection. Both classification and localization consistency regularization are introduced to ensure that the bounding boxes predicted by the student and teacher networks are consistent. Instead of sharing the network parameters with student model, our teacher model is updated using exponential moving average (EMA). Moreover, the teacher network is used to generate high-confidence pseudo labels for unlabeled data to provide student network with more supervised information. The experiment results show that the proposed method outperforms the supervised methods learned using labeled data only.