Cervical cell detection is crucial to cervical cytology screening at early stage. Currently most cervical cell detection methods use anchor-based pipeline to achieve the localization and classification of cells, e.g. faster R-CNN and YOLOv3. However, the anchors generally need to be pre-defined before training and the detection performance is inevitably sensitive to these pre-defined hyperparameters (e.g. number of anchors, anchor size and aspect ratios). More importantly, these preset anchors fail to conform to the cells with different morphology at inference phase. In this paper, we present a key-points based anchor-free cervical cell detector based on YOLOv3. Compared with the conventional YOLOv3, the proposed method applies a key-points based anchor-free strategy to represent the cells in the initial prediction phase instead of the preset anchors. Therefore, it can generate more desirable cell localization effect through refinement. Furthermore, PAFPN is applied to enhance the feature hierarchy. GIoU loss is also introduced to optimize the small cell localization in addition to focal loss and smooth L1 loss. Experimental results on cervical cytology ROI datasets demonstrate the effectiveness of our method for cervical cell detection and the robustness to different liquid-based preparation styles (i.e. drop-slide, membrane-based and sedimentation).