Cell or nucleus quantification has recently achieved state-of-the-art performance by using convolutional neural networks (CNNs). In general, training CNNs requires a large amount of annotated microscopy image data, which is prohibitively expensive or even impossible to obtain in some applications. Additionally, when applying a deep supervised model to new datasets, it is common to annotate individual cells in those target datasets for model re-training or fine-tuning, leading to low-throughput image analysis. In this paperSSS, we propose a novel adversarial domain adaptation method for cell/nucleus quantification across multimodality microscopy image data. Specifically, we learn a fully convolutional network detector with task-specific cycle-consistent adversarial learning, which conducts pixel-level adaptation between source and target domains and completes a cell/nucleus detection task. Then we generate pseudo-labels on target training data using the detector trained with adapted source images and further fine-tune the detector towards the target domain to boost the performance. We evaluate the proposed method on multiple cross-modality microscopy image datasets and obtain a significant improvement in cell/nucleus detection compared to the reference baselines and a recent state-of-the-art deep domain adaptation approach. In addition, our method is very competitive with the fully supervised models trained with all real target training labels.