  Based on the method by [K\"uc95], we give a procedure to list up all complete
intersection Calabi--Yau manifolds with respect to direct sums of irreducible
homogeneous vector bundles on Grassmannians for each dimension. In particular,
we give a classification of such Calabi--Yau 3-folds and determine their
topological invariants. We also give alternative descriptions for some of them.
