Data from the Princess Sirindhorn Neutron Monitor at Doi Inthanon, Thailand, with a vertical cutoff rigidity of 16.8 GV, were utilized to determine the diurnal anisotropy (DA) of Galactic cosmic rays (GCRs) near Earth during solar minimum conditions between 2007 November and 2010 November. We identified trains of enhanced DA over several days, which often recur after a solar rotation period (∼27 days). By investigating solar coronal holes as identified from synoptic maps and solar wind parameters, we found that the intensity and anisotropy of cosmic rays are associated with the high-speed streams (HSSs) in the solar wind, which are in turn related to the structure and evolution of coronal holes. An enhanced DA was observed after the onset of some, but not all, HSSs. During time periods of recurrent trains, the DA was often enhanced or suppressed according to the sign of the interplanetary magnetic field B, which suggests a contribution from a mechanism involving a southward gradient in the GCR density, n, and a gradient anisotropy along B × ∇n. In one non-recurrent and one recurrent sequence, an HSS from an equatorial coronal hole was merged with that from a trailing mid-latitude extension of a polar coronal hole, and the slanted HSS structure in space with suppressed GCR density can account for the southward GCR gradient. We conclude that the gradient anisotropy is a source of temporary changes in the GCR DA under solar minimum conditions, and that the latitudinal GCR gradient can sometimes be explained by the coronal hole morphology.