Accurate cell counting in microscopic images is important for medical diagnoses and biological studies. However, manual cell counting is very time-consuming, tedious, and prone to subjective errors. We propose a new density regression-based method for automatic cell counting that reduces the need to manually annotate experimental images. A supervised learning-based density regression model (DRM) is trained with annotated synthetic images (the source domain) and their corresponding ground truth density maps. A domain adaptation model (DAM) is built to map experimental images (the target domain) to the feature space of the source domain. By use of the unsupervised learning-based DAM and supervised learning-based DRM, a cell density map of a given target image can be estimated, from which the number of cells can be counted. Results from experimental immunofluorescent microscopic images of human embryonic stem cells demonstrate the promising performance of the proposed counting method.