Subject motion in brain MRI remains an unsolved problem. We propose a machine learning approach for motion correction of brain images. Our initial objective is to train a neural network to perform a motion corrected image reconstruction on image data with simulated motion artefacts. Training pairs were generated using an open source MRI data set; a unique motion profile was applied to each 2D image. A deep neural network was developed and trained with over 3000 image pairs. The images predicted by the network, from motion-corrupted k-space, have improved image quality compared to the motion corrupted images.