Despite the advancement of question answering (QA) systems and rapid improvements on held-out test sets, their generalizability is a topic of concern. We explore the robustness of QA models to question paraphrasing by creating two test sets consisting of paraphrased SQuAD questions. Paraphrased questions from the first test set are very similar to the original questions designed to test QA models’ over-sensitivity, while questions from the second test set are paraphrased using context words near an incorrect answer candidate in an attempt to confuse QA models. We show that both paraphrased test sets lead to significant decrease in performance on multiple state-of-the-art QA models. Using a neural paraphrasing model trained to generate multiple paraphrased questions for a given source question and a set of paraphrase suggestions, we propose a data augmentation approach that requires no human intervention to re-train the models for improved robustness to question paraphrasing.