Conversational question answering (CQA) is a novel QA task that requires understanding of dialogue context. Different from traditional single-turn machine reading comprehension (MRC) tasks, CQA includes passage comprehension, coreference resolution, and contextual understanding. In this paper, we propose an innovated contextualized attention-based deep neural network, SDNet, to fuse context into traditional MRC models. Our model leverages both inter-attention and self-attention to comprehend conversation context and extract relevant information from passage. Furthermore, we demonstrated a novel method to integrate the latest BERT contextual model. Empirical results show the effectiveness of our model, which sets the new state of the art result in CoQA leaderboard, outperforming the previous best model by 1.6% F1. Our ensemble model further improves the result by 2.7% F1.