Computer-assisted cervical screening is an effective method to save the doctors' workload and improve their work efficiency. Usually, the correct classification of cervical cells depends on the nuclear segmentation effect and the extraction of nuclear features. However, the precise nucleus segmentation remains a huge challenge, especially for densely distributed nucleus. Moreover, previous cellular classification methods are mostly based on morphological features of nucleus size or color. Those individual features can make accurate classification for severe lesions, but not for mild lesions. In this paper, we propose an accurate instance segmentation algorithm and propose cognition-based features to identify cervical cancer cells. Different from previous individual nucleus features, we also propose population features and cognition-based features according to the Bethesda System (TBS) for reporting cervical cytology and the diagnostic experience of the cytologists. The results showed that the segmentation achieves better success in complex situations than that by traditional segmentation algorithms. Besides, the cell classification via cognition-based features also help us find out more about less severe lesions' nuclei than that based on conventional features of individual nucleus, meaning an improvement of classification accuracy for cervical screening.