Crowdsourcing has emerged as a popular approach for collecting annotated data to train supervised machine learning models. However, annotator bias can lead to defective annotations. Though there are a few works investigating individual annotator bias, the group effects in annotators are largely overlooked. In this work, we reveal that annotators within the same demographic group tend to show consistent group bias in annotation tasks and thus we conduct an initial study on annotator group bias. We first empirically verify the existence of annotator group bias in various real-world crowdsourcing datasets. Then, we develop a novel probabilistic graphical framework GroupAnno to capture annotator group bias with an extended Expectation Maximization (EM) algorithm. We conduct experiments on both synthetic and real-world datasets. Experimental results demonstrate the effectiveness of our model in modeling annotator group bias in label aggregation and model learning over competitive baselines.