Active learning is an important technique to reduce the number of labeled examples in supervised learning. Active learning for binary classification has been well addressed. However, active learning of reject option classifier is still an unsolved problem. In this paper, we propose novel algorithms for active learning of reject option classifiers. We develop an active learning algorithm using double ramp loss function. We provide mistake bounds for this algorithm. We also propose a new loss function called double sigmoid loss function for reject option and corresponding active learning algorithm. We provide extensive experimental results to show the effectiveness of the proposed algorithms. The proposed algorithms efficiently reduce the number of label examples required.