Automation-assisted cervical screening via Pap smear or liquid-based cytology (LBC) is a highly effective cell imaging based cancer detection tool, where cells are partitioned into "abnormal" and "normal" categories. However, the success of most traditional classification methods relies on the presence of accurate cell segmentations. Despite sixty years of research in this field, accurate segmentation remains a challenge in the presence of cell clusters and pathologies. Moreover, previous classification methods are only built upon the extraction of hand-crafted features, such as morphology and texture. This paper addresses these limitations by proposing a method to directly classify cervical cells-without prior segmentation-based on deep features, using convolutional neural networks (ConvNets). First, the ConvNet is pretrained on a natural image dataset. It is subsequently fine-tuned on a cervical cell dataset consisting of adaptively resampled image patches coarsely centered on the nuclei. In the testing phase, aggregation is used to average the prediction scores of a similar set of image patches. The proposed method is evaluated on both Pap smear and LBC datasets. Results show that our method outperforms previous algorithms in classification accuracy (98.3%), area under the curve (0.99) values, and especially specificity (98.3%), when applied to the Herlev benchmark Pap smear dataset and evaluated using five-fold cross validation. Similar superior performances are also achieved on the HEMLBC (H&E stained manual LBC) dataset. Our method is promising for the development of automation-assisted reading systems in primary cervical screening.