360-degree panoramic videos have gained considerable attention in recent years due to the rapid development of head-mounted displays (HMDs) and panoramic cameras. One major problem in streaming panoramic videos is that panoramic videos are much larger in size compared to traditional ones. Moreover, the user devices are often in a wireless environment, with limited battery, computation power, and bandwidth. To reduce resource consumption, researchers have proposed ways to predict the users' viewports so that only part of the entire video needs to be transmitted from the server. However, the robustness of such prediction approaches has been overlooked in the literature: it is usually assumed that only a few models, pre-trained on past users' experiences, are applied for prediction to all users. We observe that those pre-trained models can perform poorly for some users because they might have drastically different behaviors from the majority, and the pre-trained models cannot capture the features in unseen videos. In this work, we propose a novel meta learning based viewport prediction paradigm to alleviate the worst prediction performance and ensure the robustness of viewport prediction. This paradigm uses two machine learning models, where the first model predicts the viewing direction, and the second model predicts the minimum video prefetch size that can include the actual viewport. We first train two meta models so that they are sensitive to new training data, and then quickly adapt them to users while they are watching the videos. Evaluation results reveal that the meta models can adapt quickly to each user, and can significantly increase the prediction accuracy, especially for the worst-performing predictions.