Exploiting 4D-flow magnetic resonance imaging (MRI) data to quantify hemodynamics requires an adequate spatio-temporal vector field resolution at a low noise level. To address this challenge, we provide a learned solution to super-resolve in vivo 4D-flow MRI data at a post-processing level. We propose a deep convolutional neural network (CNN) that learns the inter-scale relationship of the velocity vector map and leverages an ecient residual learning scheme to make it computationally feasible. A novel, direction-sensitive, and robust loss function is crucial to learning vector-field data. We present a detailed comparative study between the proposed super-resolution and the conventional cubic B-spline based vector-field super-resolution. Our method improves the peak-velocity to noise ratio of the flow field by 10 and 30% for in vivo cardiovascular and cerebrovascular data, respectively, for 4× super-resolution over the state-of-the-art cubic B-spline. Significantly, our method offers 10x faster inference over the cubic B-spline. The proposed approach for super-resolution of 4D-flow data would potentially improve the subsequent calculation of hemodynamic quantities.