Using single-task deep learning methods to reconstruct Magnetic Resonance Imaging (MRI) data acquired with different imaging sequences is inherently challenging. The trained deep learning model typically lacks generalizability, and the dissimilarity among image datasets with different types of contrast leads to suboptimal learning performance. This paper proposes a meta-learning approach to efficiently learn image features from multiple MR image datasets. Our algorithm can perform multi-task learning to simultaneously reconstruct MR images acquired using different imaging sequences with different image contrasts. The experiment results demonstrate the ability of our new meta-learning reconstruction method to successfully reconstruct highly-undersampled k-space data from multiple MRI datasets simultaneously, outperforming other compelling reconstruction methods previously developed for single-task learning.