We present a methodology to achieve 3D high-resolution diffusion tensor image reconstruction of the brain in moving subjects. The source data is diffusion-sensitized single-shot echo-planar images. After continuous scanning to acquire a repeated series of parallel slices with 15 diffusion directions, image registration is used to realign the images to correct for subject motion. Once aligned, the diffusion images are treated as irregularly-sampled data where each voxel is associated with an appropriately rotated diffusion direction. This data is used to estimate the diffusion tensor on a regular grid. The method has been tested on data acquired at 1.5T from adults who deliberately moved and from eight fetuses imaged in utero. Maps of apparent diffusion coefficient (ADC) were reliably produced in all cases and promising performance was achieved for fractional anisotropy maps. Results from normal fetal brains were found to be consistent with published data from premature infants of similar gestational age.