In material science and engineering, the grain structure inside a super-alloy sample determines its mechanical and physical properties. In this paper, we develop a new Multichannel Edge-Weighted Centroidal Voronoi Tessellation (MCEWCVT) algorithm to automatically segment all the 3D grains from microscopic images of a super-alloy sample. Built upon the classical k-means/CVT algorithm, the proposed algorithm considers both the voxel-intensity similarity within each cluster and the compactness of each cluster. In addition, the same slice of a super-alloy sample can produce multiple images with different grain appearances using different settings of the microscope. We call this multichannel imaging and in this paper, we further adapt the proposed segmentation algorithm to handle such multichannel images to achieve higher grain-segmentation accuracy. We test the proposed MCEWCVT algorithm on a 4-channel Ni-based 3D super-alloy image consisting of 170 slices. The segmentation performance is evaluated against the manually annotated ground-truth segmentation and quantitatively compared with other six image segmentation/edge-detection methods. The experimental results demonstrate the higher accuracy of the proposed algorithm than the comparison methods.