PurposeIn functional MRI (fMRI), faster sampling of data can provide richer temporal information and increase temporal degrees of freedom. However, acceleration is generally performed on a volume‐by‐volume basis, without consideration of the intrinsic spatio‐temporal data structure. We present a novel method for accelerating fMRI data acquisition, k‐t FASTER (FMRI Accelerated in Space‐time via Truncation of Effective Rank), which exploits the low‐rank structure of fMRI data.Theory and MethodsUsing matrix completion, 4.27× retrospectively and prospectively under‐sampled data were reconstructed (coil‐independently) using an iterative nonlinear algorithm, and compared with several different reconstruction strategies. Matrix reconstruction error was evaluated; a dual regression analysis was performed to determine fidelity of recovered fMRI resting state networks (RSNs).ResultsThe retrospective sampling data showed that k‐t FASTER produced the lowest error, approximately 3–4%, and the highest quality RSNs. These results were validated in prospectively under‐sampled experiments, with k‐t FASTER producing better identification of RSNs than fully sampled acquisitions of the same duration.ConclusionWith k‐t FASTER, incoherently under‐sampled fMRI data can be robustly recovered using only rank constraints. This technique can be used to improve the speed of fMRI sampling, particularly for multivariate analyses such as temporal independent component analysis. Magn Reson Med 74:353–364, 2015. © 2014 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.