In this work, we propose a novel deep learning reconstruction framework for rapid and accurate reconstruction of 4D flow MRI data. Reconstruction is performed on a slice-by-slice basis by reducing artifacts in zero-filled reconstructed complex images obtained from undersampled k-space. A deep residual attention network FlowRAU-Net is proposed, trained separately for each encoding direction with 2D complex image slices extracted from complex 4D images at each temporal frame and slice position. The network was trained and tested on 4D flow MRI data of aortic valvular flow in 18 human subjects. Performance of the reconstructions was measured in terms of image quality, 3-D velocity vector accuracy, and accuracy in hemodynamic parameters. Reconstruction performance was measured for three different k-space undersamplings and compared with one state of the art compressed sensing reconstruction method and three deep learning-based reconstruction methods. The proposed method outperforms state of the art methods in all performance measures for all three different k-space undersamplings. Hemodynamic parameters such as blood flow rate and peak velocity from the proposed technique show good agreement with reference flow parameters. Visualization of the reconstructed image and velocity magnitude also shows excellent agreement with the fully sampled reference dataset. Moreover, the proposed method is computationally fast. Total 4D flow data (including all slices in space and time) for a subject can be reconstructed in 69 seconds on a single GPU. Although the proposed method has been applied to 4D flow MRI of aortic valvular flows, given a sufficient number of training samples, it should be applicable to other arterial flows.