4D Flow MRI is valuable for the evaluation of cardiovascular disease, but abdominal applications are currently limited by the need for background phase error correction. We propose an automated deep learning-based method that utilizes a multichannel 3D convolutional neural network (CNN) to produce corrected velocity fields. Comparisons of arterial and venous flow, as well as flow before and after bifurcation of major abdominal vessels, show improved flow continuity with greater agreement after automated correction. Results of automated corrections are comparable to manual corrections. CNN-based corrections may improve reliability of flow measurements from 4D Flow MRI.