Cell detection is an essential task in cell image analysis. Recent deep learning-based detection methods have achieved very promising results. In general, these methods require exhaustively annotating the cells in an entire image. If some of the cells are not annotated (imperfect annotation), the detection performance significantly degrades due to noisy labels. This often occurs in real collaborations with biologists and even in public data-sets. Our proposed method takes a pseudo labeling approach for cell detection from imperfect annotated data. A detection convolutional neural network (CNN) trained using such missing labeled data often produces over-detection. We treat partially labeled cells as positive samples and the detected positions except for the labeled cell as unlabeled samples. Then we select reliable pseudo labels from unlabeled data using recent machine learning techniques; positive-and-unlabeled (PU) learning and P-classification. Experiments using microscopy images for five different conditions demonstrate the effectiveness of the proposed method. Our code is available at https://github.com/FujiiKazuma/CDFIAPLSUP.git.