In this work we study the task of image annotation, of which the goal is to describe an image using a few tags. Instead of predicting the full list of tags, here we target for providing a short list of tags under a limited number (e.g., 3), to cover as much information as possible of the image. The tags in such a short list should be representative and diverse. It means they are required to be not only corresponding to the contents of the image, but also be different to each other. To this end, we treat the image annotation as a subset selection problem based on the conditional determinantal point process (DPP) model, which formulates the representation and diversity jointly. We further explore the semantic hierarchy and synonyms among the candidate tags, and require that two tags in a semantic hierarchy or in a pair of synonyms should not be selected simultaneously. This requirement is then embedded into the sampling algorithm according to the learned conditional DPP model. Besides, we find that traditional metrics for image annotation (e.g., precision, recall and F1 score) only consider the representation, but ignore the diversity. Thus we propose new metrics to evaluate the quality of the selected subset (i.e., the tag list), based on the semantic hierarchy and synonyms. Human study through Amazon Mechanical Turk verifies that the proposed metrics are more close to the humans judgment than traditional metrics. Experiments on two benchmark datasets show that the proposed method can produce more representative and diverse tags, compared with existing image annotation methods.