In this paper, we propose a new directional 3D interpolation algorithm for brain magnetic resonance images. Typically, brain images consist of a number of 2D images. In order to reconstruct 3D objects from slices of 2D images, interpolation operation is required. In most 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 these three orthogonal coordinates may result in some information loss, particularly when gradients of pixel values have directions similar to the directions of the coordinates. In order to address this problem, we propose a new directional interpolation algorithm. In the proposed algorithm, we first perform the interpolation along two orthogonal coordinates. Typically, the two orthogonal coordinates would be the coordinates of the 2D images. And then, in order to find the best interpolation of the remaining coordinate, we search various directions that are not orthogonal to the two orthogonal coordinates using cost functions. Experiments show promising results.