4D flow MRI provides visualization and quantification of complex blood flow. However, the inherent high dimensionality leads to long acquisition times. In this work, 4D flow MRI was accelerated using the novel Low-Rank Tensor framework. To reduce the amount of unknowns, the 4D flow dataset is approximated by a Tucker decomposition, whose components are obtained from navigator and sparse data with iterative optimization exploiting sparsity after variable k-space undersampling. Using this technique, 4D flow MRI acquisition could be accelerated up to 20 times (flow phantom) and 8 times (in-vivo), while preserving measurement accuracy of high velocity magnitudes and cardiac variability.