In this paper, we propose a 3D directional interpolation algorithm for brain magnetic resonance (MR) images using neural networks. Typically, brain images consist of a number of 2D images. Although the sequences of 2D images provide basic information on structure, abnormality and etc., further processing on the sequences provides far more information. In processing 3D images, interpolation operation is one of the most widely used operations. In most conventional interpolation algorithms in the 3D space, the interpolation operation is performed separately in each coordinate that is orthogonal to each other. However, since the shape of the brain is roughly a sphere, interpolation along three orthogonal coordinates may result in some distortion, particularly in the vicinity of the boundary. In order to address this problem, we propose a new 3D interpolation algorithm. In the proposed method, we first perform the interpolation along two orthogonal coordinates. In order to find the best interpolation in the remaining coordinate, we search various directions that are not orthogonal to the two orthogonal coordinates using a cost function. Then we use neural networks to determine the final direction for interpolation. Experiments with brain MR images show improved results.