Convolutional neural networks (CNNs) have achieved success in optical flow estimation using labeled datasets, but they fail to build an internal representation to fast adapt to the specific task. On the other hand, limited by the lack of ground truth, existing CNNs-based methods suffer from high noise sensitivity and inferior generalization performance. We integrate the meta-learning technique with optical flow estimation, which can learn internal features to search optimal initial state parameters of the network. Meanwhile, we devise an enhanced network termed MetaFlow to further improve performance. MetaFlow extracts per-pixel features, builds correlation volumes for all pairs of pixels, and iteratively updates optical flow through optical flow predictor using meta-learning. In addition, we propose a meta-transfer pretraining approach to obtain initial network weights, which can efficiently avoid network overfitting. Empirical experiments on MPI Sintel and KITTI benchmarks have shown that the proposed MetaFlow achieves the state-of-the-art results and performs outstanding in challenging scenarios such as textureless regions and abrupt motions.